Research Seminar RTG 2131

 

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Winterterm 2020/21

At TU Dortmund.
 

Date Speaker Title
02.11. Holger Rauhut Structured Random Matrices in Compressive Sensing and Suprema of Chaos Processes
09.11. Nina Gantert Large deviations for lacunary sums
16.11. Vadim Gorin Infinite beta random matrix theory
23.11. Felix Pogorzelski Mathematical quasicrystals and unique ergodicity
30.11. Laszlo Erdös Edge Universality for Non-Hermitian Random Matrices
07.12. Patrik Ferrari KPZ universality in mathematics and physics
14.12. Erika Hausenblas Numerical Modelling of a stochastic Gray-Scott system
04.01. Matthias Schulte Non-standard limits for a family of autoregressive stochastic sequences
11.01. Amin Coja-Oghlan Disordered systems and random graphs
18.01. Michael Voit Limit theorems for Bessel processes of large dimensions and free convolutions
25.01. Hugo Duminil-Copin Emerging symmetries in 2D percolation
01.02. Larry Goldstein Relaxing Gaussian Assumptions in High Dimensional Statistical Procedures
08.02. Uta Freiberg Analysis on the Stretched Sierpinski Gasket

Summerterm 2020

Apr 27

Thomas Kruse, University of Giessen
Multilevel Picard approximations for high-dimensional semilinear parabolic partial differential equations

We present new approximation methods for high-dimensional PDEs and BSDEs. A key idea of our methods is to combine multilevel approximations with Picard fixed-point approximations. We prove in the case of semilinear heat equations with Lipschitz continuous nonlinearities that the computational effort of one of the proposed methods grows polynomially both in the dimension and in the reciprocal of the required accuracy. We illustrate the efficiency of the approximation methods by means of numerical simulations. The talk is based on joint works with Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Tuan Nguyen and Philippe Von Wurstemberger.

May 4

Cécile Mailler, University of Bath
Degree distribution in random simplicial complexes

In this joint work with Nikolaos Fountoulakis, Tejas Iyer and Henning Sulzbach (Birmingham), we study a random graph model introduced by Bianconi and Rahmede in 2015. This model is a simplicial complex model that generalises Apollonian networks and the random recursive trees, by, in particular, adding random weights to the nodes. For this general model, we prove limiting theorems for the degree distribution, and confirm the conjecture of Bianconi and Rahmede on the scale-free propoerties of this random graph.

May 11

Andreas Basse-O’Conner, Aarhus University
On infinite divisible laws on high dimensional spaces

Infinite divisible laws play a crucial role in many areas of probability theory. This class of laws corresponds exactly to all the possible weak limits of triangular arrays of random variables, due to the generalized central limit theorem, and hence infinite divisible laws are natural generalizations of the Gaussian laws. In this talk we will discuss properties and representations of infinite divisible probability measures on Banach spaces, with particular focus on their Lévy-Khintchine representations and their shot noise representations. We will see that these representations depend heavily on the Banach space under consideration. In particular, both the geometry of the Banach space and its “size” will play a big role. Many examples of high dimensional probability measures come from stochastic process theory, and we will illustrate the results within this framework.

May 18

Manuel Cabezas, Pontificia Universidad Católica de Chile
The totally asymmetric activated random walk model at criticality

Activated random walks is a system of particles which perform random walks and can spontaneously fall asleep, staying put. When an active particle falls on a sleeping one, the sleeping particle becomes active and continues moving. The system displays a phase transition in terms of the density of particles. If the density is small, all particles will eventually sleep forever, while, if the density is high, the system can sustain a positive proportion of active particles. In this talk we describe the critical behavior of the model in the totally asymmetric case. Joint work with Leo Rolla.

May 25 Airam Blancas Benítez, Stanford University

Coalescent models for trees within trees

Phylogenetic gene trees are contained within the branches of the species trees. In order to model genealogy backwards in time, of both, gene trees and species trees, simple exchangeable coalescent (snec) process are defined and characterized in talk. In particular, we study the coming down form infinity property for the so called nested Kingman. Finally, we present a model to include population structure in gene lineages.

June 8 Geronimo Uribe Bravo, UNAM

On the profile of trees with a given degree sequence

For a given (plane) tree $\tau$, let  $N_i$ be the quantity of individuals with $i$ descendants and define its degree sequence  as $s=(N_i)_{i\geq 1}$. We will be interested in the uniform distribution on trees whose degree sequence is $s$. We give conditions for the convergence of the profile (aka the sequence of generation sizes) as the size of the tree goes to infinity. This gives a more general formulation and a probabilistic proof of a conjecture due to Aldous for conditioned Galton-Watson trees.  Our formulation contains results in this direction obtained previously by Drmota-Gittenberger and Kersting. The technique, based on path transformations for exchangeable increment processes, also gives us a (partial) compactness criterion for the inhomogeneous continuum random tree.
Joint work with Osvaldo Angtuncio. 

June 15

Olivier Hénard, Université Paris-Sud
Parking  on critical GW trees

Lackner and Panholzer (2015) introduced the parking process on trees as a generalization of the classical parking process on the line. 
In this model, a random number of cars with mean m and variance σ2 arrive independently on the vertices of a critical Galton–Watson tree with finite variance Σ2 conditioned to be large. The cars go down the tree and try to park on empty vertices as soon as possible.  We show a phase transition depending on Θ:=(1−m)2 −Σ22 +m2 −m), confirming a conjecture by Goldschmidt and Pryzkucki (2016). Specifically, if Θ > 0, then most cars will manage to park, whereas if Θ < 0 then a positive fraction of the cars will not find a spot and exit the tree through the root. 
The proof relies on tools in percolation theory such as differential (in)equalities obtained through increasing couplings combined with the use of many-to-one lemmas and spinal decompositions of random trees.
This is joint work with Nicolas Curien (Paris Saclay).

June 22

Adrian Gonzalez Casanova, UNAM
From continuous state branching processes to coalescents

The relation between these two important families of processes has been investigated in some cases. In particular, in a a renowned paper by seven authors,  the $\beta$-coalescents are obtained as a functional of two independent $\alpha$-stable branching processes. 
Using Gillispie's sampling method, we find that an analogous relation holds for every lambda coalescent. Furthermore, functionals of independent CSBPs with different laws lead to frequency processes of coalescents with selection, mutation, efficiency and more.
This is a joint work in progress with Maria Emilia Caballero (UNAM) and Jose Luis Perez (CIMAT).

June 29

Antoine Lejay, Institut Élie Cartan de Lorraine (IECL)
Two Embeddable Markov Chain Schemes for simulating diffusions with irregular coefficients

We discuss the problem of the Monte Carlo simulation of sample paths. The Embeddable Markov Chain Schemes simulate the exact positions of a diffusion at some hitting times which are not known but only approximated. Such schemes aim at overcoming the situations in which the Euler-Maruyama scheme cannot be used, because of the presence of discontinuous coefficients, interfaces, sticky points, …
In this talk, we present two such schemes. The first one uses the explicit expressions of the resolvent kernel instead
of the density and deal with discontinuous coefficients. It leads to fast convergence. The second one generalises the Donsker approximation in presence of degenerate coefficients and appears to be fully flexible. Both schemes heavily rely on the underlying infinitesimal generator.
From joint work with Alexis Anagnostakis, Lionel Lenôtre, Géraldine Pichot and Denis Villemonnais.

July 6

Thomas Godland, University of Münster
Conical tessellations associated with Well chambers

In this talk, I consider d-dimensional random vectors Y1,,Yn that satisfy a mild general position assumption a.s. The hyperplanes

(Yi+Yj)(1i<jn),(YiYj)(1i<jn),Yi(1in)

generate a conical tessellation of the Euclidean d-space, which is closely related to the Weyl chambers of type Bn. I will present a formulas for the number of cones which holds almost surely. For a random cone chosen uniformly at random from this random tessellation, I will address expectations for a general series of geometric functionals. These include the face numbers, as well as the conical intrinsic volumes and the conical quermassintegrals. All these expectations turn out to be distribution-free.
In a similar fashion, I will shortly discuss a conical tessellations which is closely related to the Weyl chambers of type An1. I will present analogous formulas the number of cones in this tessellation and the expectations of the same geometric functionals for the random cones obtained from this random tessellation. The main ingredient in the proofs is a connection between the number of faces of the tessellation and the number of faces of the Weyl chambers of the corresponding type that are intersected by a certain linear subspace in general position.

July 13

Osvaldo Angtuncio, UNAM
On multitype random forests with a given degree sequence, the total population of branching forests and enumerations of multitype forests

In this talk, we introduce the model of uniform multitype forests with a given degree sequence (MFGDS). The construction is done using the results of Chaumont and Liu 2016, and a novel path transformation on multidimensional discrete exchangeable increment processes, which is a generalization of the Vervaat transform. By mixing the laws of MFGDS, one obtains multitype Galton-Watson (MGW) forests conditioned with the number of individuals of each type (CMGW). We also obtain the joint law of the number of individuals by types in a MGW forest, generalizing the Otter-Dwass formula. This allows us to get enumerations of multitype forests with a combinatorial structure (plane, labeled and binary forest), having a prescribed number of roots and individuals by types. Finally, under certain hypotheses, we give an easy algorithm to simulate CMGW forests, generalizing the unitype case given by Devroye in 2012. The previous results can be considered as the first step to obtain the profile of the multitype Lévy forest.

 

Winterterm 2019/20

 at Ruhr University Bochum

Oct 14 Pascal Maillard, Toulouse (France)
1-stable fluctuations of branching Brownian motion at critical temperature
Oct 21 Holger Sambale, Bielefeld
Higher order concentration of measure
Oct 28 Carina Betken, Bochum
Poisson cylinder processes: concentration inequalities and a CLT for the volume
Nov 4 Erik Broman, Uppsala (Sweden)
The Poisson cylinder process in Euclidean and Hyperbolic space
Nov 11 Nina Holden, ETH Zürich (Switzerland)
Cardy embedding of random planar maps
Nov 18 Leif Döring, Mannheim
Existence, Uniqueness and Explosion results for stable SDEs
Dec 2 Hanna Döring, Osnabrück
Crossing Numbers and Stress of Random Geometric Graphs
Dec 9 Joseph Najnudel, Bristol (UK)
On smooth mesoscopic linear statistics of the eigenvalues of random permutation matrices
Jan 6 Karen Habermann, Sorbonne Université Paris (France)
A semicircle law and decorrelation phenomena for iterated Kolmogorov loops
Jan 13 Steffen Dereich, Münster
A central limit theorem for averaged gradient descend in deep learning applications
Jan 20 Quan Shi, Mannheim
Measure-valued diffusions with Poisson-Dirichlet stationary distributions
Jan 27 George Andriopoulos, Shanghai (China)
Scaling limits of random walks in random environments on trees and related parameters

 

Summerterm 2019

at Ruhr University Bochum

Apr 8

Kristina Schubert, Dortmund, RTG
Fluctuation results for general block spin Ising models

Apr 15

Anna Gusakova, Bochum, RTG
Affine transformation of random simplex and integral geometry formulas for ellipsoid

May 6

Jere Koskela, Warwick
Asymptotic genealogies of interacting particle systems

May 13

Yuriy Nemish, Klosterneuburg, IST
Local laws for polynomials of Wigner matrices

May 20

Michael Soerensen, Kopenhagen
Diffusion bridges and estimation for SDEs with random effects

May 27

Anna Paola Todino, Bochum
Stein-Malliavin approximation for local geometric functionals of random eigenfunctions on the sphere

Jun 17

Max Fathi, Toulouse
Stein kernels, Monge-Ampere equations and the CLT

Jun 24

Miklós Kornyik, Budapest
Random matrices and orthogonal polynomials

Jul 1

Markus Reiss, Berlin
Nonparametric estimation for SPDEs via localization

Jul 8 David Damanik, Houston
The Fürstenberg-Ishii Criterion for a Positive Lyapunov Exponent and Applications to Anderson Localization
 

Winterterm 2018/19

at University Duisburg-Essen

Oct 8

Abel Klein, Irvine (USA)
Manifestations of dynamical localization in the random XXZ quantum spin chain

Oct 8 Tobias Müller, Groningen (Netherlands)
The critical probability for confetti percolation equals 1/2
Oct 15

Vitalii Konarovskyi, Leipzig
A particle model for Wasserstein type diffusion

Oct 22 PI-meeting
Oct 29

Piotr Graczyk, Angers (France)
Squared Bessel particle systems and Wishart processes

Nov 5

Vlada Limic, Strasbourg (France)
Large random graphs and excursions of Levy-type processes

Nov 12

Wioletta Ruszel, Delft (Netherlands)
A zoo of scaling limits of odometers in divisible sandpile models

Nov 19

Noemi Kurt, Berlin
Modelling the Lenski experiment

Nov 26

Tran Viet Chi, Lille (France)
Exploration of a social network by a respondent driven sampling survey

Dec 3

Martin Slowik, Berlin
Green kernel asymptotics for two-dimensional random walks among random conductances

Dec 17

Michael Hinz, Bielefeld
Hydrodynamic limits of weakly asymmetric exclusion processes on fractals

Jan 7

Sebastian Riedel, Berlin
A random dynamical system for stochastic delay differential equations

Jan 14

Mike Keane, Leiden (Netherlands)
The World of Fibonacci, Thue-Morse and Toeplitz Substitutions

Jan 21

Thomas Mikosch, Copenhagen (Denmark) and Bochum
Regular variation and heavy-tail large deviations for time series

Jan 28

Johannes Heiny, Bochum (RTG)
Assessing the dependence of high-dimensional time series via autocovariances and autocorrelations

Summerterm 2018

at Ruhr University Bochum

Apr 16
Universality in Non-Hermitian Random Matrix Theory: Fixed Trace Ensembles
Apr 19
Ciprian Tudor, Lille (France)
Variation of the solution to the wave equation
Apr 23
Floquet Theory for Markov processes and a nonlinear generalisation
Apr 30
Normal approximation of U-statistics via contractions
May 7
Ilya Molchanov, Bern (Switzerland)
The semigroup of metric measure spaces and its infinitely divisible measure
May 14
Beatrice-Helen Vritsiou, Ann Arbor (Michigan, USA)
Selberg-type integrals and the variance conjecture for the Schatten classes
May 28
The Wright-Fisher model with selection in a random environment
Jun 4
Eliza O’Reilly, Austin (Texas, USA)
Reach of Repulsion for Determinantal Point Processes in High Dimensions
Jun 18
Yacine Barhoumi-Andréani, Zurich (Switzerland)
On the mid-coefficient of a random unitary matrix
Jun 25
Paolo Pigato, Berlin
Estimation of piecewise-constant coefficients in a stochastic differential equation
Jul 2
Priscilla Greenwood, Vancouver (Canada)
Quasi-patterns of synchronization produced by a Mexican hat coupling of quasi-cycles
Jul 9
Daniel Hug, Karlsruhe
Geometric Stability, mass transportation and stochastic geometry
Jul 16
Piotr Graczyk, Angers (France)
Squared Bessel particle systems and Wishart processes

Winterterm 2017/18

at Ruhr University Bochum

Oct 16
Peter Mörters, Köln
Metastability of the contact process on evolving scale-free networks
Oct 23
Ivan Veselic, Dortmund
Glivenko Cantelli and Ergodic Theorem on groups
Nov 6
Anita Winter, Duisburg-Essen
Brownian motion on graph-like metric spaces and the cover time bound
Nov 13
Dunkl processes and particle systems: dynamics due to the exchange interaction
Nov 20
Masha Gordina, Connecticut
Stochastic Analysis and Geometric Functional Inequalities
 
Chiranjib Mukherjee, Münster
Recent developments in compact large deviation theory and applications to statistical mechanics
Nov 27
Frank Aurzada, Darmstadt
Persistence probabilities for fractional processes
Dec 4
The Pitman theorem and random walks on trees and hyperbolic spaces
Dec 11
Mira Shamis, London
The Curie-Weiss model at complex temperature
Dec 18 RTG Feedback meeting
Jan 8
Günter Last, Karlsruhe
How to find an extra excursion in Brownian motion
Jan 11
Quasi-infinitely divisible distributions
Jan 15
Simone Warzel, München
Localization-delocalization transitions in effective random matrix models
Jan 22
On the MM*-estimate for isotropic convex bodies: upper bounds for the mean norm and the mean width
Jan 29-30 Workshop Statistical Mechanics

 

Summerterm 2017

at TU Dortmund

April 24th  Sandra Kliem, University of Duisburg-Essen
Travelling wave solutions to the KPP equation with branching noise
May, 8th   Karl-Theodor Sturm, University of Bonn
Heat flow, optimal transport, and Ricci curvature on metric measure spaces
May, 15 th

Wolfgang König, TU Berlin
The principal part of the spectrum of a random Schrödinger operator in a large box

May, 22nd Elena Pulvirenti University of Bonn

Metastability for the Widom-Rowlinson model

May, 29th

Joscha Prochno, University of Hull, UK
On operator norms of Gaussian random matrices

June, 8th

René Schilling, University Dresden
Distance Covariance

June, 12th Jean-Yves Welschinger, University of Lyon
Expected topology of a random subcomplex in a simplicial complex
June, 19th
Anne Estrade, University of Paris
A test of Gaussianity based on the Euler characteristic of excursion sets
June, 26th

Christian Bender, University Saarbrücken
Discretizing Malliavin Calculus

July, 3rd

Paul Doukhan, University Cergy-Pontoise
Discrete trawl model processes with long range dependence

July, 10th

Lisa Hartung, New York University
The Structure of Extreme Level Sets in Branching Brownian Motion

July, 17th Larry Goldstein, UCLA
Non asymptotic distributional bounds for the Dickman approximation of the running time of the Quickselect algorithm

 

Wintertherm 2016/17

at Ruhr University Bochum

October 24th  Sebastian Andres, University of Cambridge, UK
Diffusion processes on Branching Brownian Motion
November 7th   David Croydon, University of Warwick, UK
Scaling limits of stochastic processes accociated with resistance forms
November 14th

Ngoc Mai Tran, University of Bonn
Iterated Gilbert mosaics and Poisson tropical plane curves

November 21st Christoph Külske, University of Bochum

Gibbs-non Gibbs transitions for point particles under time-evolution: the Widom-Rowlinson model under spin flip

November 28th Jan Nagel, TU München
Large deviations for random matrices and sum rules
December 5th Julian Grothe, University of Bochum
Gaussian polytopes and simplices - a cumulant based approach
December 12th Uta Freiberg, University of Stuttgart

Spectral asymptotics on random Sierpinski gaskets

December 19th RTG-Feedback meeting
January 9th
Matthias Schulte, University of Bern
Malliavin-Stein method, stochastic geometry and beyond
January 16th Sandra Palau Calderon, University of Bath
Generalisations of continuous-state branching processes
January 23rd Sara Mazzonetto, University of Potsdam, Lille
Exact simulation of Brownian diffusions with drift admitting jumps
January 30th Elisabeth Werner, Case Western Reserve University Cleveland
Approximation of convex bodies by polytopes

 

Summertherm 2016

at University Duisburg-Essen

April 18th Jeannette Woerner, University of Dortmund
An introduction to fractional processes and related limit theorems
April 25th

Martin Hutzenthlaler, University of Duisburg-Essen
A coercivity-type condition for SPDEs with additive white noise

May 2nd

Pierre Calka, University of Rouen
Asymptotic results for random polytope

May 9th  Angelika Rohde, University of Bochum
Spectral analysis of high-dimensional sample covariance matrices
with missing observations
May 23rd Maurizia Rossi, University of Luxemburg
Non-universality of nodal length distribution for arithmetic random
waves
May 30th Margherita Disertori, University of Bonn
History dependent stochastic processes and non linear sigma models
June 6th Imre Barany, Hungarian Academy of sciences Budapest
On the randomized integer convex hull
June 13th Markus Heydenreich, LMU München
Scale-free percolation
June 20th
Ehsan Azmoodeh, University of Helsinki
An attempt to small deviations
June 27th Holger Kösters, Bielefeld
Products of Independent Random Matrices: From Singular Values to Eigenvalues
July 4th Alexander Drewitz, University of Köln
The maximal particle of branching random walk in spatially random
branching environment
July 11th Sebastian Scholtes, University of Aachen
Old and new on sets of positive reach
July 18th Hui He, University of Beijing
From Galton-Watson trees to Levy trees: Scaling limits, pruning process and reduced trees

 

Wintertherm 2015/16

at Ruhr University Bochum

October 26

Sander Dommers (University of Bochum)
Critical exponents of theIsing model on random graphs

November 2

Bram Petri (University of Bonn)
Random surfaces

November 9

Claudio Dursatanti (University of Bochum)
Normal approximations of linear and nonlinear statistics over the sphere

November 16

Nicola Kistler (University of Frankfurt)
Extremes of random fields: a multi-scale approach

November 23

Tobias Fissler (University of Bern)
Testing the maximal rank of the volatility process for continuous diffusions observed with noise

November 30

Richard Kraaij (University of Delft)
Large deviations for trajectories of weakly interacting Markov jump processes

December 7

Matthias Löwe (University of Münster)
On the spectrum of random matrices with correlated entries

December 14

Sabine Jansen (University of Bochum)
Statistical mechanics at low temperature

December 21

Mark Podolskij (University of Aarhus)
Limit theorems for stationary increments Levy driven moving averages

January 11

Fabian Gerle (University of Duisburg-Essen)
An invariance principle for random walks on graphs

January 18

Vaidotas Characiejus (University of Bochum)
Asymptotic Behaviour of Functional Linear Processes with Long Memory

January 25

Raghid Zeineddine (University of Dortmund)
On a new Itô type formula

January 1st

Vaidotas Characiejus(university of Bochum)
Asymptotic Behaviour of Functional Linear Processes with Long Memory

February 8

Arnulf Jentzen (ETH Zürich)
Mild stochastic calculus in infinite dimensions