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Autumn Semester 2013

Date / Time Speaker Title Location
18 September 2013
17:15-19:00 		Adrien Kassel
ETH Zürich
Event Details

Seminar on Stochastic Processes

Title A natural loop model on surfaces
Speaker, Affiliation Adrien Kassel, ETH Zürich
Date, Time 18 September 2013, 17:15-19:00
Location HG G 43
Abstract I will describe a discrete loop model on graphs. It has rich combinatorial properties (e.g. it can be sampled exactly and has a determinantal integrable structure) and a natural continuum scaling limit for graphs embedded on Riemannian surfaces. The limiting loop model satisfies a spatial Markov property and conformal covariance.
A natural loop model on surfacesread_more
HG G 43
25 September 2013
17:15-19:00 		Alexander Vandenberg-Rodes
UC Irvine
Event Details

Seminar on Stochastic Processes

Title The Lee-Yang theorem in probability and statistical physics
Speaker, Affiliation Alexander Vandenberg-Rodes, UC Irvine
Date, Time 25 September 2013, 17:15-19:00
Location HG G 43
Abstract First proved for the Ising model of magnetization, the Lee-Yang Circle Theorem is a remarkable restriction on location of zeros of the partition (generating) function, and is the starting point for a large body of research into the nature of phase transitions in many models of statistical physics. In this talk I will give a brief overview of the Lee-Yang theory, which can be nicely expressed in terms of the stability properties of linear transformations through the recent work of J. Borcea and P. Branden. I'll then discuss a nice application to the symmetric exclusion process.
The Lee-Yang theorem in probability and statistical physicsread_more
HG G 43
2 October 2013
17:15-18:15 		Nicolas Broutin
INRIA Paris
Event Details

Seminar on Stochastic Processes

Title The scaling limit of the minimum spanning tree of a complete graph
Speaker, Affiliation Nicolas Broutin, INRIA Paris
Date, Time 2 October 2013, 17:15-18:15
Location HG G 43
Abstract We consider a complete graph weighted with iid uniform weights and build the minimum spanning tree $T_n$. The tree $T_n$ has a attracted a lot of attention, but most informations known about its structure are local, even the famous result of Frieze saying that the total weight of converges to $\zeta(3)$. We are interested in the global structure of as $n\to\infty$, and consider it as a random metric space on equipped with the graph distance $d_{T_n}$. We show that there exists a limit compact metric space $M$ such that $(T_n, n^{-1/3}d_{T_n})$ converges in distribution to $M$. The metric space is a continuum random tree, that we prove different from Aldous' CRT using arguments relying on its fractal dimension. This is a joint work with L. Addario-Berry, C. Goldschmidt and G. Miermont.
The scaling limit of the minimum spanning tree of a complete graphread_more
HG G 43
9 October 2013
17:15-18:15 		Victor Rivero
CIMAT Guanajuato
Event Details

Seminar on Stochastic Processes

Title Quasi-stationary distributions and Yaglom limits for self-similar Markov processes
Speaker, Affiliation Victor Rivero, CIMAT Guanajuato
Date, Time 9 October 2013, 17:15-18:15
Location HG G 43
Abstract We discuss the existence and characterization of quasi-stationary distribu- tions and Yaglom limits of self-similar Markov processes that reach 0 in nite time. By Yaglom limit, we mean the existence of a deterministic function g and a non-trivial probability measure  such that the process rescaled by g and con- ditioned on non-extinction converges in distribution towards . We will see that a Yaglom limit exits if and only if the extinction time at 0 of the process is in the domain of attraction of an extreme law and we will then discuss separately three cases, according whether the extinction time is in the domain of attraction of a Gumbel law, a Weibull law or a Frchet law. In each of these cases, necessary and sucient conditions on the parameters of the underlying Lvy process are given for the extinction time to be in the required domain of attraction. The limit of the process conditioned to be positive is then characterized by a multiplicative equation which is connected to a factorization of the exponential distribution in the Gumbel case, a factorization of a Beta distribution in the Weibull case and a factorization of a Pareto distribution in the Frchet case. This approach relies partly on results on the tail distribution of the extinction time, which is known to be distributed as the exponential integral of a Lvy process. In that aim, some new results on its asymptotic behaviour are given. We will also discuss how the factorization of exponential, beta and Pareto distributions can be used to obtain explicit information about the law of the rst hitting time of zero or of the Yaglom limit.
Quasi-stationary distributions and Yaglom limits for self-similar Markov processesread_more
HG G 43
16 October 2013
17:15-18:15 		Ron Rosenthal
ETH Zürich
Event Details

Seminar on Stochastic Processes

Title Quenched invariance principle for simple random walk on clusters of correlated percolation models
Speaker, Affiliation Ron Rosenthal, ETH Zürich
Date, Time 16 October 2013, 17:15-18:15
Location HG G 43
Abstract We derive a quenched invariance principle for simple random walk on the unique infinite cluster for a general class of percolation models on $\mathbb{Z}^d$, $d\geq2$. This includes models with long-range correlations such as random interlacements in dimension $d\geq3$ at every level, as well as for the vacant set of random interlacements and the level sets of the Gaussian free field in the regime of the so-called local uniqueness. An essential ingredient of our proof is a new isoperimetric inequality for this type of correlated percolation models. This is a joint work with Eviatar Procaccia and Artëm Sapozhnikov.
Quenched invariance principle for simple random walk on clusters of correlated percolation modelsread_more
HG G 43
23 October 2013
17:15-18:15 		Wei-Kuo Chen
University of Chicago
Event Details

Seminar on Stochastic Processes

Title On Gaussian inequalities for product of functions
Speaker, Affiliation Wei-Kuo Chen, University of Chicago
Date, Time 23 October 2013, 17:15-18:15
Location HG G 43
Abstract Gaussian inequalities have played important roles in various scientific areas. In this talk, we will present simple algebraic criteria that yield sharp Holder types of inequalities for the product of functions of Gaussian random vectors with arbitrary covariance structure. As an application, we will explain how our results yield several famous inequalities in functional geometry, such as, the Brascamp-Lieb inequality, the sharp Young inequality, etc. This part of the talk is based on the recent joint work with N. Dafnis and G. Parious. Along this direction, we will discuss a conjecture on the convexity of the Parisi functional arising from the study of the Sherrington-Kirkpatrick model in spin glass.
On Gaussian inequalities for product of functionsread_more
HG G 43
6 November 2013
17:15-18:15 		Matthias Birkner
Universität Mainz
Event Details

Seminar on Stochastic Processes

Title Directed random walk on an oriented percolation cluster
Speaker, Affiliation Matthias Birkner, Universität Mainz
Date, Time 6 November 2013, 17:15-18:15
Location HG G 43
Abstract We consider a directed random walk on the backbone of the infinite cluster generated by supercritical oriented percolation, and exhibit suitable regeneration structures to obtain a law of large numbers and a quenched central limit theorem. The walk can be interpreted as the space-time embedding of the ancestral lineage of a sampled individual in the stationary discrete-time contact process. Extensions to more general population models, leading to random walks in correlated space-time environments, and also to several walkers are of interest in population genetic applications. I will discuss approaches to extend the results in this direction. Based on joint work, in part in progress, with Jiri Cerny, Andrej Depperschmidt and Nina Gantert.
Directed random walk on an oriented percolation clusterread_more
HG G 43
27 November 2013
17:15-18:15 		Alois Panholzer
TU Wien
Event Details

Seminar on Stochastic Processes

Title Analytic combinatorics approaches to study discrete stochastic processes
Speaker, Affiliation Alois Panholzer, TU Wien
Date, Time 27 November 2013, 17:15-18:15
Location HG G 43
Abstract A basic combinatorial approach to analyze the behaviour of discrete stochastic processes relies on the exact enumeration of combinatorial objects with certain properties. In many cases such random structures allow an exact recursive description, which is the basis of a further analytic approach often involving complex analytic techniques. Although the results obtained by such an approach sometimes lack in generality, when applicable, one often gets a very precise description. We will illustrate this method by some concrete examples including the so-called hiring problem, some parking problems as well as the analysis of simple evolutionary algorithms.
Analytic combinatorics approaches to study discrete stochastic processesread_more
HG G 43
11 December 2013
17:15-18:15 		Xue-Mei Li
University of Warwick
Event Details

Seminar on Stochastic Processes

Title Stochastic flows and Derivative flows for SDE with irregular coefficients
Speaker, Affiliation Xue-Mei Li, University of Warwick
Date, Time 11 December 2013, 17:15-18:15
Location HG G 43
Abstract We consider a SDE with the following properties: (1) elliptic but not strictly elliptic (2) The coefficients belong to a local Sobolev space, in particular unbounded. We prove that there is a global smooth stochastic flow that is in W^{1,p}_{loc} for sufficiently small time. This is a critical case for regularity of the solution with respect to the initial value. We also construct a solution to the `linearize SDE'. This is joint work with X. Chen.
Stochastic flows and Derivative flows for SDE with irregular coefficientsread_more
HG G 43
18 December 2013
17:15-18:15 		Tal Orenshtein
Weizmann Institute of Science and TU Munich
Event Details

Seminar on Stochastic Processes

Title Excitements in one dimension
Speaker, Affiliation Tal Orenshtein, Weizmann Institute of Science and TU Munich
Date, Time 18 December 2013, 17:15-18:15
Location HG G 43
Abstract Excited random walk (also called Cookie walk) is a self interacting discrete time stochastic process on graphs so that the transition probability is given not only by the location, but also by the number of past visits to that location. The one-dimensional lattice case has a special structure. We shall discuss some old and new results. Joint with Gideon Amir and Noam Berger.
Excitements in one dimensionread_more
HG G 43

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Organizers: Jean Bertoin, Erwin Bolthausen, Ashkan Nikeghbali, Pierre Nolin, Martin Schweizer, Alain-Sol Sznitman

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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