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.

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.

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.

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.

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.

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. 

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).

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).

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.

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

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

(Y_i+Y_j)⊥(1≤i<j≤n),(Y_i−Y_j)⊥(1≤i<j≤n),Y⊥i(1≤i≤n)

generate a conical tessellation of the Euclidean d-space, which is closely related to the Weyl chambers of type B_n. 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 A_n−1. 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.

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.

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

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

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

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

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

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

Miklós Kornyik, Budapest
Random matrices and orthogonal polynomials

Markus Reiss, Berlin
Nonparametric estimation for SPDEs via localization

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

Vitalii Konarovskyi, Leipzig
A particle model for Wasserstein type diffusion

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

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

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

Noemi Kurt, Berlin
Modelling the Lenski experiment

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

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

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

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

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

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

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

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

Metastability for the Widom-Rowlinson model

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

René Schilling, University Dresden
Distance Covariance

Christian Bender, University Saarbrücken
Discretizing Malliavin Calculus

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

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

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

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

Spectral asymptotics on random Sierpinski gaskets

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

Pierre Calka, University of Rouen
Asymptotic results for random polytope

October 26

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

Bram Petri (University of Bonn)
Random surfaces

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

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

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

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

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

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

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

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

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

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

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

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