# Publications

## List of Publications

### Submitted:

Josué Nussbaumer, Anita Winter, The algebraic α-Ford tree under evolution, arXiv: 2006.09316, preprint.

L. Osorio, A. Winter, Two level branching model for virus population under cell division, arXiv:2004.14352, preprint.

Stefan Ankirchner, Thomas Kruse, Wolfgang Löhr, Mikhail Urusov, Properties of the EMCEL scheme for approximating irregular diffusions, arXiv: 2004.10316, preprint.

J. Cerný, A. Klimovsky, Markovian dynamics of exchangeable arrays, arXiv:1810.13165, preprint.

R. Meizis, Convergence of metric two-level measure spaces, arxiv:1805.00853, preprint.

A. Greven, A. Sturm, A.Winter, I. Zähle,  Multi-type spatial branching models for local self-regulation, I: Construction and an exponential duality, arXiv:1509.0402, preprint.

A. Greven, V. Limic, Anita Winter, Coalescent processes arising in the study of diffusive clustering, arXiv:0703875, preprint.

R. van der Hofstad, S. Kliem, J. S.H. van Leeuwaarden, Cluster tails for critical power-law inhomogeneous random graphs, arXiv:1404.1727, preprint.

Z. Kabluchko, A. Klimovsky, Generalized random energy model at complex temperatures, arXiv:1402.2142, preprint.

### Publications:

#### 2021

G. Berzunza, A. Sturm, A. Winter, Trait-dependent branching particle systems with competition and multiple offspring, Electronic Journal of Probability Vol. 26, No. 153 (2021), 1-41, paper

W. Löhr, A. Winter, Spaces of algebraic measure trees and triangulations of the circle, Bulletin de la Société Mathématique de France, 149 (1) (2021), p. 1-63 pdf.

#### 2020

O. Angtuncio-Hernández, Multidimensional Random Walks Conditioned to Stay Ordered via Generalized Ladder Height Functions, XIII Symposium on Probability and Stochastic Processes, Springer International Publishing, 2020, p. 39-65, pdf.

W. Löhr, L. Mytnik, A. Winter, The Aldous chain on cladograms in the diffusion limit, Annals of Probability, Volume 48, Number 5 (2020), 2565-2590, paper.

Anton Klimovsky, Stochastic models of inhomogeneous complex systems: Emergence of multi-scale hierarchies, Habilitation Thesis, University of Duisburg-Essen 2020, pdf.

#### 2019

S.Kliem, A. Winter, Evolving phylogenies of trait-dependent branching with mutation and competition. Part I: Existence, Stochastic Processes and their Applications, vol. 129 (2019), issue 12, 4837-4877, print.

#### 2018

A. Greven, F. den Hollander, A. Klimovsky, The hierarchical Cannings process in random environment, ALEA, Lat. Am. J. Probab. Math. Stat. 15 (2018), 295-351, paper.

L. Hartung, A. Klimovsky, The phase diagram of the complex branching Brownian motion energy model, Electronic Journal of Probability, Vol. 23 (27) (2018), 1–27, paper.

A. Greven, F. den Hollander, A. Klimovsky, The hierarchical Cannings process in random environment, ALEA, Lat. Am. J. Probab. Math. Stat. 15 (2018), 295-351, paper.

#### 2017:

S. Athreya, W. Löhr, A.Winter, Invariance principle for variable speed random walks on trees, Annals of Probability, Vol. 45 (2) (2017), 625-667, arXiv:1404.6290, preprint.

S. Kliem, Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support, Stochastic Processes and their Applications, Vol. 127 (2017), 385-418, arXiv:1508.00687, paper.

#### 2016:

A. Greven, R Sun, A.Winter, Continuum Space Limit of the Genealogies of Interacting Fleming-Viot Prozesses on Z, Electronic Journal of Probability, Vol. 21, No. 58 (2016), 1-64, paper.

S. Athreya, W. Löhr, A.Winter, The gap between Gromov-vague and Gromov-Hausdorff-vague topology, Stochastic Processes and their Applications, Vol. 126 (9) (2016), 2527-2553, arXiv:1407.6309, preprint.

E. Aïdékon, R. van der Hofstad, S. Kliem and J. .H. van Leeuwaarden, Large deviations for power-law thinned Lévy processes, Stochastic Processes and their Applications, 126 (5) (2016), 1353-1384, arXiv:1404.1692, preprint.

W. Löhr, T. Rippl, Boundedly finite measures: Separation and convergence by an algebra of functions, Electronic Communications in Probability, Vol. 21 (2016), 1-16,  arXiv:1603.05818, preprint.

##### 2015:

W. Löhr, G. Voisin, A. Winter, Convergence of bi-measure R-trees and the pruning process, Annales de l'Institut Henri Poincaré (B) Probababilités et Statistiques, Vol. 51, No. 4 (2015), 1342-1368, arXiv:1304.6035, preprint.

S. Kliem, W. Löhr, Existence of mark functions in marked metric measure spaces, Electronic Journal of Probability, Vol 20 (73) (2015), 1-24, paper.

N. Ay, W. Löhr, The Umwelt of an Embodied Agent - A Measure-Theoretic Definition, Theory in Biosciences, Vol. 134 (3) (2015) 105-116, paper.

L. Hartung, A. Klimovsky, The glassy phase of the complex branching Brownian motion energy model, Electronic Communications in Probability, Vol. 20 (78) (2015), 1–15, paper.

##### 2014:

A.Greven, F. den Hollander, S. Kliem and A. Klimovsky, Renormalisation of hierarchically interacting Cannings processes, ALEA, Lat. Am. J. Probab. Stat. 11 (1) (2014), 43-140, paper.

S. Kliem, A compact containment result for nonlinear historical superprocess approximations for population models with trait-dependence, Electronic Journal of Probability, Vol. 19 (97) (2014), 1-13, paper.

Z. Kabluchko, A. Klimovsky, Complex Random Energy Model: Zeros and Fluctuations, Probability Theory and Related Fields, Vol. 158 (2014), 159-196, paper.

#### 2013:

S. Athreya, M. Eckhoff, A. Winter, Brownian motion on real trees, Transaction American Mathematics Society, Vol. 365 (2013), 3115-3150, arXiv:1102.3215, preprint.

A. Greven, P. Pfaffelhuber, A. Winter, Tree-valued resampling dynamics: Martingale problems and applications, Probability Theory and Related Fields, Vol. 155 (3-4) (2013), 789-838, paper.

W. Löhr, Equivalence of Gromov-Prohorov- and Gromov's Box-Metric on the Space of Metric Measure Spaces, Electronic Communications in Probability, Vol. 18 (17) (2013), 1-10, paper.

#### 2012:

W. Löhr, A. Szkoła, N. Ay, Process Dimension of Classical and Non-Commutative Processes, Open Systems & Information Dynamics, Vol. 19 (1) (2012), 1-14, 2012. paper.

W. Löhr, Predictive Models and Generative Complexity, Journal of System Science and Complexity, Vol. 25 (1) (2012), 30-45, paper.

A. Klimovsky, High-dimensional Gaussian fields with isotropic increments seen through spin glasses, Electronic Communications in Probability, Vol. 17 (2012), 1-14, paper

#### 2011:

S. Kliem, Long-term behaviour of a cyclic catalytic branching system, Stochastic Processes and their Applications., Vol. 121 (2011), 357-377, paper.

S. Kliem, Convergence of Rescaled Competing Species Processes to a Class of SPDEs, Electronic Journal of Probability, Vol. 16 (2011), 618--657, paper.

A. Klimovsky, Towards renormalisation of the hierarchically interacting heavy-tailed Lambda-Cannings models, Oberwolfach Reports, Vol. 8(1) (2011), 806–809, paper.

#### 2009:

A. Greven, P. Pfaffelhuber, A. Winter, Convergence in distribution of random metric measure spaces: The Lambda-coalescent measure tree, Probability Theory and Related Fields, Vol. 145 (1-2) (2009), 285-322, arXiv:0609801, preprint.

A. Greven, L. Popovic, A.Winter, Genealogy of catalytic branching models, Annals of Applied Probability, Vol.19, No. 3 (2019), 1232-1272, arXiv:0606313, preprint.

S. Kliem, Degenerate Stochastic Differential Equations for Catalytic Branching Networks, Annales de l'Institut Henri Poincaré (B) Probababilités et Statistiques, Vol. 45 (2009), 943--980, arXiv:0802.0035, preprint.