# Research Seminar RTG 2131

## 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 −Σ2(σ2 +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)⊥(1≤i

## 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 Martin Venker, Bochum 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 Thomas Kriecherbauer, Bayreuth Floquet Theory for Markov processes and a nonlinear generalisation Apr 30 Christian Döbler, Luxemburg 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 Maite Wilke-Berenguer, Berlin 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 Sergio Andraus, Tokyo 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 Philippe Bougerol, Paris 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 Alexander Lindner, Ulm Quasi-infinitely divisible distributions Jan 15 Simone Warzel, München Localization-delocalization transitions in effective random matrix models Jan 22 Apostolos Giannopoulos, Athens 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