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Seminar on Stochastic Processes
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Spring Semester 2017
Note: The highlighted event marks the next occurring event.
Date / Time | Speaker | Title | Location | |
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22 February 2017 17:15-19:00 |
Sarah Penington University of Oxford |
The front location in branching Brownian motion with decay of mass | 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. | ||||
1 March 2017 17:15-19:00 |
Alessandra Caraceni University of Bath |
Self-Avoiding Walks on Random Quadrangulations | 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. | ||||
8 March 2017 17:15-19:00 |
Arvind Singh Université Paris-Sud |
The contact process on random graphs, via cumulative merging | 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. | ||||
22 March 2017 17:15-18:15 |
Antii Knowles Université de Genève |
Spectral radii of sparse random matrices | 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. | ||||
29 March 2017 17:15-18:15 |
Nicolas Matte Bon ETH Zürich |
Extensive amenability of group actions | 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. | ||||
5 April 2017 17:15-18:15 |
Max Fathi Université de Toulouse |
Stein kernels and the central limit theorem | 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. | ||||
12 April 2017 17:15-18:15 |
Bastien Mallein Universität Zürich |
Branching random walk in random environment | 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. | ||||
26 April 2017 17:15-18:15 |
Charles Bordenave Université de Toulouse |
Spectrum of random graphs | 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. | ||||
3 May 2017 17:15-18:15 |
Stefano Olla Université Paris Dauphine |
Entropic hypocoercivity and hydrodynamic limits | 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. | ||||
10 May 2017 17:15-18:15 |
Hugo Vanneuville Université Lyon 1 |
Exceptional times for percolation under exclusion dynamics | 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. | ||||
17 May 2017 17:15-18:15 |
Bruno Shapira Université de Marseille |
Capacity of random walk, Swiss cheese, and folding | 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. | ||||
24 May 2017 17:15-18:15 |
Fabio Martinelli Università di Roma Tre |
Bootstrap percolation and interacting particle systems with kinetic constraints: critical time and length scales | 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). |
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