Departement Mathematik

Seminar on stochastic processes

Members of the probability group are involved in co-organizing remote specialized seminars that take place on Tuesdays and Thursdays:

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Frühjahrssemester 2017

Datum / Zeit Referent:in Titel Ort
22. Februar 2017
17:15-19:00 		Sarah Penington
University of Oxford
Details

Seminar on Stochastic Processes

Titel The front location in branching Brownian motion with decay of mass
Referent:in, Affiliation Sarah Penington, University of Oxford
Datum, Zeit 22. Februar 2017, 17:15-19:00
Ort Y27 H 25
Abstract We add a competitive interaction between nearby particles in a branching Brownian motion (BBM). Each particle has a mass, which decays at rate proportional to the local mass density at its location. The total mass increases through branching events. In standard BBM, we may define the front location at time t as the greatest distance of a particle from the origin. For the model with masses, it makes sense to instead define the front displacement as the distance at which the local mass density drops from Θ(1) to o(1). We can show that in a weak sense this front is ~ c t^{1/3} behind the front for standard BBM. I will discuss the proof of this result and progress on further results related to this model. This is joint work with Louigi Addario-Berry.
The front location in branching Brownian motion with decay of massread_more
Y27 H 25
1. März 2017
17:15-19:00 		Alessandra Caraceni
University of Bath
Details

Seminar on Stochastic Processes

Titel Self-Avoiding Walks on Random Quadrangulations
Referent:in, Affiliation Alessandra Caraceni, University of Bath
Datum, Zeit 1. März 2017, 17:15-19:00
Ort Y27 H 25
Abstract The local limit of random quadrangulations (UIPQ) and the local limit of quadrangulations with a simple boundary (the simple boundary UIHPQ) are two very well studied objects. We shall see how the simple boundary UIHPQ relates to an annealed model of self-avoiding walk on random quadrangulations, and how metric information obtained for the UIHPQ can be used to study quantities such as the displacement of the self-avoiding walk from the origin, as well as to ultimately investigate how the biasing of random quadrangulations by the number of their self-avoiding walks affects their local limit.
Self-Avoiding Walks on Random Quadrangulationsread_more
Y27 H 25
8. März 2017
17:15-19:00 		Arvind Singh
Université Paris-Sud
Details

Seminar on Stochastic Processes

Titel The contact process on random graphs, via cumulative merging
Referent:in, Affiliation Arvind Singh, Université Paris-Sud
Datum, Zeit 8. März 2017, 17:15-19:00
Ort Y27 H 25
Abstract The contact process is a classical interacting particle system which models the spread of a disease inside a network. For bounded degree graphs, there always exists a positive critical infection rate below which the infection vanishes almost-surely. On the other hand, if the graph has unbounded degree, it may happen that the infection survives for any infection rate. In this talk, I will introduce a percolation model on set of vertices of the graph called "cumulatively merged partition" and I will try to explain how the existence of an infinite cluster relates to the existence of a sub-critical infection phase for the contact process. Joint work with L. Ménard.
The contact process on random graphs, via cumulative mergingread_more
Y27 H 25
22. März 2017
17:15-18:15 		Antii Knowles
Université de Genève
Details

Seminar on Stochastic Processes

Titel Spectral radii of sparse random matrices
Referent:in, Affiliation Antii Knowles, Université de Genève
Datum, Zeit 22. März 2017, 17:15-18:15
Ort Y27 H 12
Abstract We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erd\H{o}s-R\'enyi graphs. For the Erd\H{o}s-R\'enyi graph $G(n,d/n)$, our results imply that the smallest and second-largest eigenvalues of the adjacency matrix converge to the edges of the support of the asymptotic eigenvalue distribution provided that $d \gg \log n$. This establishes a crossover in the behaviour of the extremal eigenvalues around $d \sim \log n$. Our results also apply to non-Hermitian sparse random matrices, corresponding to adjacency matrices of directed graphs. Joint work with Florent Benaych-Georges and Charles Bordenave.
Spectral radii of sparse random matricesread_more
Y27 H 12
29. März 2017
17:15-18:15 		Nicolas Matte Bon
ETH Zürich
Details

Seminar on Stochastic Processes

Titel Extensive amenability of group actions
Referent:in, Affiliation Nicolas Matte Bon, ETH Zürich
Datum, Zeit 29. März 2017, 17:15-18:15
Ort Y27 H 12
Abstract A group is amenable if the spectral radius of any symmetric random walk on it is equal to one. This is only one among the many equivalent characterisations of this property, that make it play a role in many aspects of group theory. Nevertheless, deciding wether a group is amenable or not can be a difficult problem. Extensive amenability is a property of group actions, first considered by Juschenko and Monod, that leads to a method to prove amenability of groups. I will explain this property and give a a probabilistic reformulation of it, then explain this method and illustrate it by proving amenability of some groups of interval exchange transformations. Finally I will highlight the current limits of this method and some related open questions. Talk based on a joint work with Juschenko, Monod, and de la Salle.
Extensive amenability of group actionsread_more
Y27 H 12
5. April 2017
17:15-18:15 		Max Fathi
Université de Toulouse
Details

Seminar on Stochastic Processes

Titel Stein kernels and the central limit theorem
Referent:in, Affiliation Max Fathi, Université de Toulouse
Datum, Zeit 5. April 2017, 17:15-18:15
Ort Y27 H 12
Abstract Stein kernels are a way of measuring how far a given measure is from being gaussian, defined via integration by parts formulas. I will present an existence result and some applications, including a quantitative central limit theorem with an optimal dependence on the dimension. The proof will be based on simple arguments of calculus of variations. Joint work with Thomas Courtade and Ashwin Pananjady.
Stein kernels and the central limit theoremread_more
Y27 H 12
12. April 2017
17:15-18:15 		Bastien Mallein
Universität Zürich
Details

Seminar on Stochastic Processes

Titel Branching random walk in random environment
Referent:in, Affiliation Bastien Mallein, Universität Zürich
Datum, Zeit 12. April 2017, 17:15-18:15
Ort Y27 H 12
Abstract In this article we consider a branching random walk defined as follows. It starts with a unique individual located at position 0 at time 0. At each integer time n, we choose a point process law $P_n$ at random. Then every individual currently alive dies, giving birth to children according to i.i.d. point processes with law $P_n$. We take interest in the impact of this random environment on the maximal displacement of the process.
Branching random walk in random environmentread_more
Y27 H 12
26. April 2017
17:15-18:15 		Charles Bordenave
Université de Toulouse
Details

Seminar on Stochastic Processes

Titel Spectrum of random graphs
Referent:in, Affiliation Charles Bordenave, Université de Toulouse
Datum, Zeit 26. April 2017, 17:15-18:15
Ort Y27 H 12
Abstract In this general talk, we will review the notion of spectral measures of a graph. We will then explore some of the connections between the local geometry of a random graph and its spectrum. The talk will be partially based on the lecture notes available at http://www.math.univ-toulouse.fr/~bordenave/coursSRG.pdf.
Spectrum of random graphsread_more
Y27 H 12
3. Mai 2017
17:15-18:15 		Stefano Olla
Université Paris Dauphine
Details

Seminar on Stochastic Processes

Titel Entropic hypocoercivity and hydrodynamic limits
Referent:in, Affiliation Stefano Olla, Université Paris Dauphine
Datum, Zeit 3. Mai 2017, 17:15-18:15
Ort Y27 H 12
Abstract Entropic hypocoercivity provides estimates on regularity independent of the dimensions of the system. It seems to be the right tool to extend relative entropy methods to degenerate dynamics where noise acts only on velocities.
Entropic hypocoercivity and hydrodynamic limitsread_more
Y27 H 12
10. Mai 2017
17:15-18:15 		Hugo Vanneuville
Université Lyon 1
Details

Seminar on Stochastic Processes

Titel Exceptional times for percolation under exclusion dynamics
Referent:in, Affiliation Hugo Vanneuville, Université Lyon 1
Datum, Zeit 10. Mai 2017, 17:15-18:15
Ort Y27 H 12
Abstract Start with an initial critical percolation configuration in the plane and let it evolve in time according to an exclusion process with kernel |x-y|-(2+α). In a joint work with Christophe Garban, we prove that, if α < 217/816, then there exist exceptional times for which an infinite component appears in the percolation configuration (the result holds for site percolation on the triangular lattice). In this talk, we will first sketch the proof of the analogous result in the i.i.d. case (i.e. where sites evolve independently from each other) that goes back to Schramm-Steif, 2010 and Garban-Pete-Schramm, 2010. Then, we will explain what are the new obstacles in the dependent case.
Exceptional times for percolation under exclusion dynamicsread_more
Y27 H 12
17. Mai 2017
17:15-18:15 		Bruno Shapira
Université de Marseille
Details

Seminar on Stochastic Processes

Titel Capacity of random walk, Swiss cheese, and folding
Referent:in, Affiliation Bruno Shapira, Université de Marseille
Datum, Zeit 17. Mai 2017, 17:15-18:15
Ort Y27 H 12
Abstract We will review recent results on the localization phenomena of the random walk path under the polymer measure with weight proportional to the range, in the critical case, and see how the capacity of the range enters into the picture. Joint work with Amine Asselah and Perla Sousi.
Capacity of random walk, Swiss cheese, and foldingread_more
Y27 H 12
24. Mai 2017
17:15-18:15 		Fabio Martinelli
Università di Roma Tre
Details

Seminar on Stochastic Processes

Titel Bootstrap percolation and interacting particle systems with kinetic constraints: critical time and length scales
Referent:in, Affiliation Fabio Martinelli, Università di Roma Tre
Datum, Zeit 24. Mai 2017, 17:15-18:15
Ort Y27 H 12
Abstract Recent years have seen a great deal of progress in understanding the behaviour of bootstrap percolation models, a particular class of monotone cellular automata. In the two dimensional lattice there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behaviour (length and time scales). Mu ch less is known for their non-monotone stochastic counterpart, namely kinetically constrained models (KCM). In a KCM the state of each vertex which could be infected by the bootstrap percolation rules is resampled (independently among the vertices) at rate one by tossing a p-coin. In particular infection can also heal, hence the non-monotonicity. Besides their connection with bootstrap percolation, KCMs have an strong interest in their own : as p ↓ 0 they display some of the most striking features of the liquid/glass transition, a major and still largely open problem in condensed matter physics. In this talk, after an introductory first part, I shall discuss (i) some recent conjectures relating the universality behaviour of critical KCMs to their bootstrap percolation counterpart and (ii) some very recent progresses towards proving the above conjectures. Joint project with C. Toninelli (Paris VII) and R. Morris (IMPA).
Bootstrap percolation and interacting particle systems with kinetic constraints: critical time and length scalesread_more
Y27 H 12

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