# Oberseminar Wahrscheinlichkeitstheorie und andere Vorträge im Wintersemester 2013/14

**Organisers**: Nina Gantert (TUM), Hans-Otto Georgii (LMU), Franz Merkl (LMU), Silke Rolles (TUM), Vitali Wachtel (LMU), Gerhard Winkler (Helmholtz Zentrum München)

**Talks**:

**Friday**, 11th October 2013, 15:00, LMU, room B 349, Theresienstr. 39, Munich

Benedikt Rehle (Ludwig-Maximilians-Universität Munich, Germany)

Title: Biased random walks on Galton-Watson trees

**Monday**, 21th October 2013, 16:30, LMU, room B 251, Theresienstr. 39, Munich

Prof. Dr. Vladimir A. Vatutin (Steklov Mathematical Institute, Moscow, Russia)

Title: Subcritical branching processes in random environment

Abstract is available here.

**Thursday**, 31st October 2013

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 4th November 2013

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 11th November 2013,16:30, LMU, room B 251, Theresienstr.39, Munich

Prof. Dr. Dima Korshunov (Sobolev Institute of Mathematics)

Title: Extremal Behavior of Gaussian Chaos

Abstract: For a given centered d-dimensional Gaussian random vector $\xi$ and a homogeneous function $h:R^d\to R$ we investigate the extremal behavior of the Gaussian chaos $h(\xi)$; particular examples are the determinant of a Gaussian matrix and the Gaussian orthogonal ensemble. Using a direct probabilistic asymptotic method, we investigate both the subexponentiality and the asymptotic behavior of the tail distribution of $h(\xi)$ and its density at infinity and then discuss possible extensions for some general $\xi$ with radial representation. (Joint work with E. Hashorva and V. I. Piterbarg.)

**Monday**, 2nd December 2013

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 13th January 2014, 17:15, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (subsequent to Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM)

Dr. Alberto Chiarini (TU Berlin)

Title: Invariance principle for diffusions in random environment

Abstract: Diffusions in heterogeneous media (media with impurities) can frequently be described by its effective behaviour. This means that there is a homogeneous medium, the effective medium, whose diffusive properties are close to those of the real inhomogeneous medium when measured on long space-time scales. A process of averaging or homogenization takes place so that the complicated small scale structure of the material is replaced by an asymptotically equivalent homogeneous structure. We shall discuss the classical results by Papanicolaou-Varadhan, Kozlov and others which concern homogenenization of diffusion processes in a stationary and ergodic environment, which also include periodic and almost periodic coefficients as special case.

**Monday**, 20th January 2014, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück

Dr. Christian Döbler (Technische Universität München, Germany)

Title: Distributional transformations in Stein's method

Abstract: Distributional transformations play a large role in Stein's method of computing explicit bounds on the error in distributional convergence. This is done by coupling the random variable of interest with another random variable having the transformed distribution and rewriting the terms resulting from Stein's equation. We review known transformations like the size bias and zero bias transformations and explain their use in Stein's method. Furthermore we present new abstract theorems on existence and uniqueness of distributional transformations with certain properties, which generalize earlier results by Goldstein and Reinert. Finally, we hint at possible applications of our theory, comprising random walk models.

**Monday**, 27th January 2014,16:30, LMU, room B 251, Theresienstr.39, Munich

Prof. Dr. Sergey Foss (School of Mathematical & Computer Sciences, Edinburgh, UK)

Title: Limit theorems for a random directed graph.

Abstract: I start with a stochastic directed graph on the integers whereby a directed edge between i and a larger integer j exists with probability p that may depend on the distance j-i, and there is no edges from bigger to smaller integers. Edge lengths L(i,j) may be constants or i.i.d. random variables. We introduce also a complementary "infinite bin" model. We study the asymptotics for the maximal path length in a long chunk of the graph. Under certain assumptions, the model has a regenerative structure and, in particular, the SLLN and the CLT follow. Otherwise, we obtain scaling laws and asymptotic distributions expressed in terms of a "continuous last-passage percolation" model on [0,1]. If time allows, I introduce multi-dimensional extensions of the model and discuss similar models.

**Monday**, 3rd February 2014

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Wednesday**, 12th February 2014,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück

Prof. Dr. Alessandra Faggionato (Università degli Studi di Roma "La Sapienza", Italy)

Title: The East process as model for glassy systems.

Abstract:The East process is a Markov chain describing the evolution of an interacting particle system on the lattice Z^d, where transitions are possible only if a suitable geometric constraint is locally satisfied by the particle system. In particular, it belongs to the class of kinetically constrained processes, introduced to model and investigate glassy materials. The rigorous analysis of the East process, started with Aldous and Diaconis in the one dimensional case, has lead in the last years to several results, even confuting some physical conjectures. In the seminar we will focus on time-scale separation and dynamical heterogeneity, and present some recent results for the higher dimensional case obtained in collaboration with P. Chleboun and F. Martinelli.

How to get to Garching-Hochbrück