Seminar on Stochastic Processes

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Spring Semester 2011

Date / Time

Speaker

Title

Location

23 February 2011
17:15-18:15

Taizo Chiyonobu

Event Details

Seminar on Stochastic Processes

Title	A limit formula for a class of Gibbs measures with mean field interactions
Speaker, Affiliation	Taizo Chiyonobu,
Date, Time	23 February 2011, 17:15-18:15
Location	Y27 H 25
Abstract	Let X_i, i=1,2, , , be a real valued i.i.d. variables with a compactly supported density. We give an asymptotic evaluation of E[ exp( -sum_{i,j=1}^n V(X_i, X_j) ) ] up to the factor (1+o(1)) as n goes to infinity, under certain assumptions on V. As an application of this result, we prove a limit formula for a class of Gibbs measures with pairwise interactions V. Bolthausen and Kusuoka&Tamura considered the similar problem in the mid-80's in the case the energy is divided by n. We resort our analysis to the property of Gaussian measures on path spaces and apply Landau-Shepp-Fernique-type estimate to obtain our result.

A limit formula for a class of Gibbs measures with mean field interactionsread_more

Y27 H 25

2 March 2011
17:15-18:15

Noemi Kurt
TU Berlin

Event Details

Seminar on Stochastic Processes

Title	Entropic repulsion of a Laplacian interface model in subcritical dimensions
Speaker, Affiliation	Noemi Kurt, TU Berlin
Date, Time	2 March 2011, 17:15-18:15
Location	Y27 H 25

Entropic repulsion of a Laplacian interface model in subcritical dimensions

Y27 H 25

9 March 2011
17:15-18:15

Dr. Balázs Ráth
ETH Zurich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	On the connectivity and transience of random interlacements
Speaker, Affiliation	Dr. Balázs Ráth, ETH Zurich, Switzerland
Date, Time	9 March 2011, 17:15-18:15
Location	Y27 H 25
Abstract	We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is the random interlacement at level u of Sznitman. The present talk summarizes recent joint work with Artem Sapozhnikov (ETH). We investigate how this countable collection of doubly infinite trajectories are actually interlaced: we show that almost surely every two points of the random interlacement are connected via at most ceiling(d/2) trajectories, and that this number is optimal. With a variant of this connectivity argument we also prove that the graph induced by the random interlacements is almost surely transient. Our results hold for all d >=3 and all u>0.

On the connectivity and transience of random interlacementsread_more

Y27 H 25

* 14 March 2011
16:00-17:00

Sylvia Serfaty
Université Paris 6

Event Details

Seminar on Stochastic Processes

Title	2D Classical Coulomb gas and the renormalized energy
Speaker, Affiliation	Sylvia Serfaty, Université Paris 6
Date, Time	14 March 2011, 16:00-17:00
Location	Y27 H 12
Abstract	In joint work with Etienne Sandier, we study the statistical mechanics of a two-dimensional classical Coulomb gas, a particular case of which also correspond to the Ginibre ensemble, a random matrix model. We connect the problem to the "renormalized energy" W, a Coulombian interaction for an infinite set of points in the plane that we introduced in connexion to the Ginzburg-Landau model, and whose minimum is expected to be achieved by the "Abrikosov" triangular lattice. We obtain a next order asymptotic expansion of the partition function, an various characterizations of the behavior of the system at the microscopic scale. When the temperature tends to zero we show the system tends to ``crystallize" to a minimizer of W.

2D Classical Coulomb gas and the renormalized energy read_more

Y27 H 12

16 March 2011
17:15-18:15

Dr. Stefan Tappe
ETH Zurich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	SPDEs in Hilbert spaces: Geometry and numerics
Speaker, Affiliation	Dr. Stefan Tappe, ETH Zurich, Switzerland
Date, Time	16 March 2011, 17:15-18:15
Location	Y27 H 25
Abstract	We study stochastic partial differential equations in Hilbert spaces driven by a Wiener process and a Poisson random measure. Within this framework, we provide invariance conditions for finite dimensional submanifolds and establish convergence rates for Wong-Zakai approximations.

SPDEs in Hilbert spaces: Geometry and numericsread_more

Y27 H 25

23 March 2011
17:15-18:15

Volker Betz
University of Warwick

Event Details

Seminar on Stochastic Processes

Title	Spatial random permutations and Bose-Einstein condensation (part of a minicourse)
Speaker, Affiliation	Volker Betz, University of Warwick
Date, Time	23 March 2011, 17:15-18:15
Location	Y27 H 25

Spatial random permutations and Bose-Einstein condensation (part of a minicourse)

Y27 H 25

30 March 2011
17:15-18:15

Joseph Najnudel
University of Zurich

Event Details

Seminar on Stochastic Processes

Title	A unitary extension of virtual permutations
Speaker, Affiliation	Joseph Najnudel, University of Zurich
Date, Time	30 March 2011, 17:15-18:15
Location	Y27 H 25

A unitary extension of virtual permutations

Y27 H 25

6 April 2011
17:15-18:15

Michael Benaim
Université de Neuchâtel

Event Details

Seminar on Stochastic Processes

Title	Stochastic approximation and learning in games
Speaker, Affiliation	Michael Benaim, Université de Neuchâtel
Date, Time	6 April 2011, 17:15-18:15
Location	Y27 H 25

Stochastic approximation and learning in games

Y27 H 25

13 April 2011
17:15-18:15

Pierre-Loic Meliot
Université Marne-la-Vallée

Event Details

Seminar on Stochastic Processes

Title	Title T.B.A.
Speaker, Affiliation	Pierre-Loic Meliot, Université Marne-la-Vallée
Date, Time	13 April 2011, 17:15-18:15
Location	Y27 H 25

Title T.B.A.

Y27 H 25

20 April 2011
17:15-18:15

Frank den Hollander
University of Leiden, The Netherlands

Event Details

Seminar on Stochastic Processes

Title	The parabolic Anderson model in a dynamic random environment
Speaker, Affiliation	Frank den Hollander, University of Leiden, The Netherlands
Date, Time	20 April 2011, 17:15-18:15
Location	Y27 H 25

The parabolic Anderson model in a dynamic random environment

Y27 H 25

* 5 May 2011
17:15-18:15

Johan Tykesson
Weizmann Institute, Rehovot

Event Details

Seminar on Stochastic Processes

Title	Random interlacements and amenability
Speaker, Affiliation	Johan Tykesson, Weizmann Institute, Rehovot
Date, Time	5 May 2011, 17:15-18:15
Location	HG G 19.2
Abstract	We consider the model of random interlacements on transient graphs, which was first introduced by A-S. Sznitman in arXiv:0704.2560 for the special case of Z^d (with d > 2). There it was shown that on Z^d: for any intensity u > 0, the interlacement set is almost surely connected. It turns out that for transient, transitive graphs, the above property holds if and only if the graph is amenable. In particular, we show that in non-amenable transitive graphs, for small values of the intensity u, the interlacement set has infinitely many infinite clusters. Results concerning the phase when the interlacement set is connected will also be discussed. This is joint work with Augusto Teixeira, ENS Paris.

Random interlacements and amenabilityread_more

HG G 19.2

11 May 2011
17:15-18:15

Christophe Garban
ENS Lyon

Event Details

Seminar on Stochastic Processes

Title	Magnetization field at criticality in the Ising model
Speaker, Affiliation	Christophe Garban, ENS Lyon
Date, Time	11 May 2011, 17:15-18:15
Location	Y27 H 25
Abstract	If one considers an NN grid with independent coin flips \sigma_x in {-1,1} at each vertex, it is well known that the renormalized field N^{-1}\sum_x \sum_x \delta_{x/N} converges as N goes to infinity to a Gaussian white noise in the square [0,1]^2. More precisely for each "nice" subset A of this square, the field measured in A is a Gaussian random variable with variance the area of A. The aim of this talk is to study what happens when the coin flips are no longer independent of each other. This situation has been considered in various contexts and one cannot hope for "universality" result as in the iid case. In particular, one has to precise what type of dependency structure one is interested in. In this talk, I will focus on some famous distributions which arise in statistical mechanics and in particular on the case where the coin flips \sigma_x are defined to be the spins of an Ising model on the NN grid. In this context, the sum over the spins corresponds to the so called magnetization field. Away from the critical point, it is known that this magnetization field (properly renormalized) converges also towards a Gaussian white noise. It remains to understand the magnetization field at criticality. In a joint work with Federico Camia and Chuck Newman, we prove the following facts: (i) at T=T_c, the discrete magnetization fields have a unique scaling limit. (ii) This limit is non-Gaussian. (iii) The limit has an explicit conformally covariant structure.

Magnetization field at criticality in the Ising modelread_more

Y27 H 25

18 May 2011
17:15-18:15

Alexander Fribergh
Courant Institute, New York

Event Details

Seminar on Stochastic Processes

Title	Phase transition for the speed of the biased random walk on the supercritical percolation cluster
Speaker, Affiliation	Alexander Fribergh, Courant Institute, New York
Date, Time	18 May 2011, 17:15-18:15
Location	Y27 H 25
Abstract	We prove the sharpness of the phase transition for speed in the biased random walk on the supercritical percolation cluster on Zd. That is, for each d≥2, and for any supercritical parameter p>pc, we prove the existence of a critical strength for the bias, such that, below this value, the speed is positive, and, above the value, it is zero. We identify the value of the critical bias explicitly, and, in the sub-ballistic regime, we find the polynomial order of the distance moved by the particle. Each of these conclusions is obtained by investigating the geometry of the traps that are most effective at delaying the walk. A key element in proving our results is to understand that, on large scales, the particle trajectory is essentially one-dimensional; we prove such a dynamic renormalization statement in a much stronger form than was previously known.

Phase transition for the speed of the biased random walk on the supercritical percolation clusterread_more

Y27 H 25

25 May 2011
17:15-18:15

Ofer Zeitouni
Weizmann Institute

Event Details

Seminar on Stochastic Processes

Title	The Einstein relation for biased random walks on Galton Watson trees
Speaker, Affiliation	Ofer Zeitouni, Weizmann Institute
Date, Time	25 May 2011, 17:15-18:15
Location	Y27 H 25

The Einstein relation for biased random walks on Galton Watson trees

Y27 H 25

26 May 2011
17:15-18:15

Ivan Corwin
Courant Institute

Event Details

Seminar on Stochastic Processes

Title	The geometric RSK correspondence and Whittaker functions
Speaker, Affiliation	Ivan Corwin, Courant Institute
Date, Time	26 May 2011, 17:15-18:15
Location	Y27 H 25
Abstract	Consider a matrix of real, positive weights distributed independently as inverse-gamma random variables. We explain Kirillov's geometric Robinson Schensted-Knuth correspondence and prove that the push-forward of this product measure under the correspondence has a particularly nice structure which allows for many exact calculations. Underlying this structure is an algebraic identity in the form of an intertwining relationship between two Markov kernels, and underlying the exact calculations is the fact that Whittaker functions diagonalize the resulting Markov chain. As an application we compute the Laplace transform for the partition function of a positive temperature, discrete directed polymer model with inverse-gamma weights, generalizing some of Johansson's work on last passage percolation. We present this within the wider context of the Kardar-Parisi-Zhang equation and universality class.

The geometric RSK correspondence and Whittaker functionsread_more (CANCELLED)

Y27 H 25

1 June 2011
17:15-18:15

Alexander Novikov
University of Technology, Sydney

Event Details

Seminar on Stochastic Processes

Title	An approach to calculating asymptotic variance of Bayesian estimators
Speaker, Affiliation	Alexander Novikov, University of Technology, Sydney
Date, Time	1 June 2011, 17:15-18:15
Location	Y27 H 25
Abstract	An analytic expression for the asymptotic variance of Pitman estimators for a location parameter in discrete and continuous-time framework is obtained. The expression is given in terms of the integral functional of Limit Likelihood Ratio Process (LLRP). In particular when LLRP is the geometric Brownian motion the general formula obtained allows to express the asymptotic variance in terms of the Riemann zeta- function.

An approach to calculating asymptotic variance of Bayesian estimatorsread_more (CANCELLED)

Y27 H 25

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Organizers: Erwin Bolthausen, Jiri Cerny, Ashkan Nikeghbali, Martin Schweizer, Alain-Sol Sznitman

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