Seminar on Stochastic Processes

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Autumn Semester 2010

Date / Time

Speaker

Title

Location

22 September 2010
17:15-18:15

Dr. Artem Sapozhnikov
ETH Zurich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Non-contractible cycles in percolation on high-dimensional tori
Speaker, Affiliation	Dr. Artem Sapozhnikov, ETH Zurich, Switzerland
Date, Time	22 September 2010, 17:15-18:15
Location	HG G 43
Abstract	In this talk, we consider critical Bernoulli percolation on high-dimensional tori. We discuss recent results on the existence of open non-contractible cycles. This is a joint work with Remco van der Hofstad (TU Eindhoven)

Non-contractible cycles in percolation on high-dimensional toriread_more

HG G 43

29 September 2010
17:15-18:15

Dr. Alexander Drewitz
ETH Zurich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Survival Probability of a Random Walk Among a Poisson System of Moving Traps
Speaker, Affiliation	Dr. Alexander Drewitz, ETH Zurich, Switzerland
Date, Time	29 September 2010, 17:15-18:15
Location	HG G 43
Abstract	We review some old and new results on the survival probability of a random walk among a Poisson system of moving traps on the lattice, which can also be interpreted as the solution of a parabolic Anderson model with a random time-dependent potential. Furthermore, we compute the sub-exponential rate of decay of the annealed survival probability in dimensions one and two, and establish an exponential decay in higher dimensions. In addition, we show that the quenched survival probability always decays exponentially. A key ingredient is what is known in the physics literature as the Pascal principle, which asserts that the annealed survival probability is maximised if the random walk stays at a fixed position. This is joint work with Jürgen Gärtner, Alejandro F. Ramírez and Rongfeng Sun.

Survival Probability of a Random Walk Among a Poisson System of Moving Trapsread_more

HG G 43

6 October 2010
17:15-18:15

Nathanael Berestycki
Cambridge

Event Details

Seminar on Stochastic Processes

Title	Asymptotic behaviour of near-critical branching Brownian motion
Speaker, Affiliation	Nathanael Berestycki, Cambridge
Date, Time	6 October 2010, 17:15-18:15
Location	HG G 43
Abstract	Consider a system of particles that perform branching Brownian motion with negative drift \sqrt(2-\eps) and are killed upon hitting zero. Initially, there is just one particle at x. Kesten (1978) proved that the system survives if and only if \eps>0. In this talk I shall describe recent joint work with Julien Berestycki and Jason Schweinsberg concerning the limiting behaviour of this process as \eps tends to 0. In particular we establish sharp asymptotics for the limiting survival probability as a function of the starting point x. Moreover, the limiting genealogy between individuals from this population is shown to have a characteristic time scale of order \eps^{-3/2}. When time is measured in these units we show that the geometry of the genealogical tree converges to the Bolthausen-Sznitman coalescent. This is closely related to a set of conjectures by Brunet, Derrida and Simon.

Asymptotic behaviour of near-critical branching Brownian motionread_more

HG G 43

13 October 2010
17:15-18:15

Dr. Yan Dolinsky
ETH Zurich, Switzerland

Event Details

Seminar on Stochastic Processes

Title	Applications of Strong Approximations Theorems to Optimal Stopping
Speaker, Affiliation	Dr. Yan Dolinsky, ETH Zurich, Switzerland
Date, Time	13 October 2010, 17:15-18:15
Location	HG G 43
Abstract	We derive error estimates for multinomial approximations of optimal stopping values with payoff processes which are Lipschitz functionals of the (multidimensional) Brownian motion. Our main tool is the strong approximations theorems for i.i.d. random vectors which were obtained by Sakhanenko.

Applications of Strong Approximations Theorems to Optimal Stoppingread_more

HG G 43

20 October 2010
17:15-18:15

Charles Bordenave
Toulouse

Event Details

Seminar on Stochastic Processes

Title	Spectrum of non-hermitian heavy-tailed random matrices
Speaker, Affiliation	Charles Bordenave, Toulouse
Date, Time	20 October 2010, 17:15-18:15
Location	HG G 43
Abstract	This is a joint work with Pietro Caputo (Roma 3) and Djalil Chafaï (Paris Est). Consider an n x n random matrix whose entries are i.i.d. complex random variables in the domain of attraction of an alpha-stable law, with 0< alpha <2. We establish a heavy tailed counterpart of the circular law. Namely, as n goes to infinity, we prove that, properly rescaled, the empirical distribution of the eigenvalues converges almost surely to a limiting measure. In contrast with the Hermitian case, we find that this limiting measure is not heavy tailed. Our proof combines Aldous' objective method with Tao and Vu's approach to Girko's Hermitization using logarithmic potentials.

Spectrum of non-hermitian heavy-tailed random matricesread_more

HG G 43

27 October 2010
17:15-18:15

Hubert Lacoin
Rome

Event Details

Seminar on Stochastic Processes

Title	Crossing a repulsive interface: slowing of the dynamic and metastability phenomenon
Speaker, Affiliation	Hubert Lacoin, Rome
Date, Time	27 October 2010, 17:15-18:15
Location	HG G 43
Abstract	We study a simple heat-bath type dynamic for a simple model of polymer interacting with an interface. The polymer is a nearest neighbor path in ℤ, and the interaction is modelled by energy penalties/bonuses given when the path touches 0. This dynamic has been studied by D. Wilson for the case without interaction, then by Caputo et al. for the more general case. When the interface is repulsive, the dynamic slows down due to the appearance of a bottleneck in the state space, moreover, the systems exhibits a metastable behavior, and, after time rescaling, behaves like a two-state Markov chain. (joint work with P. Caputo, F. Martinelli, F. Simenhaus and F.L. Toninelli)

Crossing a repulsive interface: slowing of the dynamic and metastability phenomenonread_more

HG G 43

3 November 2010
17:15-18:15

Event Details

Seminar on Stochastic Processes

Title	No seminar
Speaker, Affiliation
Date, Time	3 November 2010, 17:15-18:15
Location	HG G 43

No seminar

HG G 43

* 10 November 2010
15:15-16:15

Michael Hinz
Jena

Event Details

Seminar on Stochastic Processes

Title	Semigroups, potential spaces and applications to (S)PDE
Speaker, Affiliation	Michael Hinz, Jena
Date, Time	10 November 2010, 15:15-16:15
Location	HG G 19.2
Abstract	The paper studies perturbed semilinear parabolic partial (pseudo-) differential equations on $\sigma$-finite measure spaces under low smoothness assumptions. We obtain results on existence, uniqueness and regularity. The hypotheses are formulated in terms of the semigroup, regularity is measured by means of abstract potential spaces. Being a priori analytic, our results allow to investigate related stochastic partial differential equations in the almost sure pathwise sense. For example we can study (fractional) semilinear heat equations driven by fractional Brownian noises on metric measure spaces. (joint with Martina Zähle and Elena Issoglio)

Semigroups, potential spaces and applications to (S)PDEread_more

HG G 19.2

17 November 2010
17:15-18:15

Max von Renesse
TU Berlin

Event Details

Seminar on Stochastic Processes

Title	Ergodic properties of stochastic curve shortening flow
Speaker, Affiliation	Max von Renesse, TU Berlin
Date, Time	17 November 2010, 17:15-18:15
Location	HG G 43
Abstract	We introduce a continuum (SPDE) model of motion by curvature of a (1 + 1)-dimensional membrane subject to random perturbations by e.g. a Kunita type isotropic flow. In the additive noise case ergodicity of the corresponding Markov semigroup can be established using the Lower-Bound-Technique by Komorowski, Peszat and Szarek. Refined a-priori estimates on the invariant measure allow to deduce polynomial mixing. Based on joint works with A. Es-Sarhir (Berlin) and W. Stannat (Darmstadt)

Ergodic properties of stochastic curve shortening flowread_more

HG G 43

* 24 November 2010
14:15-18:15

Event Details

Seminar on Stochastic Processes

Title	Swiss Probability Seminar
Speaker, Affiliation
Date, Time	24 November 2010, 14:15-18:15
Location	Universität Bern

Swiss Probability Seminar

Universität Bern

1 December 2010
17:15-18:15

Hugo Duminil-Copin
Geneva

Event Details

Seminar on Stochastic Processes

Title	Critical temperature of the square lattice Potts model
Speaker, Affiliation	Hugo Duminil-Copin, Geneva
Date, Time	1 December 2010, 17:15-18:15
Location	HG G 43
Abstract	In this talk, we derive the critical temperature of the q-state Potts model on the square lattice (q ≥ 2). More precisely, we consider a geometric representation of the Potts model, called the random-cluster model. Spin correlations of the Potts model get rephrased as connectivity properties of the random-cluster model. The critical temperature of the Potts model is therefore related to the critical point of the random-cluster model. For the later, a duality relation allows us to compute the critical value using a crossing estimate (similar to the celebrated Russo-Seymour-Welsh theory for percolation) and a sharp threshold theorem. This result has many applications in the field and we will briefly mention some of them at the end of the talk. This is a joint work with V. Beffara.

Critical temperature of the square lattice Potts modelread_more

HG G 43

8 December 2010
17:15-18:15

Taizo Chiyonobu
Kwansei Gakuin University

Event Details

Seminar on Stochastic Processes

Title	A limit formula for a class of Gibbs measures with mean field interactions
Speaker, Affiliation	Taizo Chiyonobu, Kwansei Gakuin University
Date, Time	8 December 2010, 17:15-18:15
Location	HG G 43
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(− ∑_i,j=1ⁿ 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 (CANCELLED)

HG G 43

15 December 2010
17:15-18:15

Christophe Sabot
Lyon

Event Details

Seminar on Stochastic Processes

Title	The environment viewed from the particle for random walks in Dirichlet environment
Speaker, Affiliation	Christophe Sabot, Lyon
Date, Time	15 December 2010, 17:15-18:15
Location	HG G 43
Abstract	The environment viewed from the particle has been a powerful tool in the investigation of random conductance models. For (non-reversible) random walks in random environment the problem of the equivalence of the static and dynamic points of view is understood only in a few cases. The case of Dirichlet environment, which corresponds to the case where the transition probabilities at each site are iid Dirichlet random variables, is particularly interesting since its annealed law corresponds to the law of a reinforced random walk. In this talk, we will characterize, for Dirichlet environments in dimension larger or equal to 3, the cases where the static and dynamic points of view are equivalent. We can deduce from this a complete characterization of the ballistic regimes in dimension larger or equal to 3. The proof is based on crucial property of statistical invariance by time reversal valid for the class of Dirichlet environments.

The environment viewed from the particle for random walks in Dirichlet environmentread_more

HG G 43

* 20 December 2010
17:15-18:15

Alexander Stauffer
Berkeley

Event Details

Seminar on Stochastic Processes

Title	Detection and Percolation in a Mobile Environment
Speaker, Affiliation	Alexander Stauffer, Berkeley
Date, Time	20 December 2010, 17:15-18:15
Location	HG G 26.3
Abstract	Motivated by mobile wireless networks we consider a random graph over R², where nodes are given by a Poisson point process and perform independent Brownian motions, and edges are kept between pairs of nodes within distance r of each other. Combining ideas from stochastic geometry, coupling and multi-scale analysis, we obtain precise asymptotics for detection (the time until a given target is within distance r to some node of the graph) and percolation (the time until a given node belongs to the infinite connected component of the graph). (This is a joint work with Yuval Peres, Alistair Sinclair and Perla Sousi.)

Detection and Percolation in a Mobile Environmentread_more

HG G 26.3

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

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