# Oberseminar Wahrscheinlichkeitstheorie und andere Vorträge im Wintersemester 2014/15

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

**Minicourse** on orthogonal polynomial ensembles by Maurice Duits (Stockholm University, Stockholm, Sweden) is starting **Tuesday**, 4^{th} November 2014.

Click here for information.

**Talks**:

**Monday**, 13^{th} October 2014,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Dr. Angelica Pachon-Pinzon (University of Turin, Italy)

Title: On the relation between the preferential attachment, Simon and Yule models

Abstract: Click here.

**Monday**, 27^{th} October 2014,16:30, LMU, room B 251, Theresienstr. 39, Munich

Antonia Löffler (LMU, Mathematisches Institut der Universität München)

Title: Problem of disruption in discrete time with geometric distribution

**Monday**, 27^{th} October 2014

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 17^{th} November 2014,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Dr. Anita Behme (TUM)

Title: On the mapping associated to exponential functionals of L\'evy processes.

Abstract: For a given bivariate L\'evy process $(\xi,\eta)$ the random variable $\int_0^\infty e^{-\xi_{s-}} d\eta_s$, whenever it exists, is called the exponential functional $(\xi,\eta)$. Its distribution appears in various applications, e.g. as the stationary solution of a generalized Ornstein–Uhlenbeck process. In this talk, we shall be interested in properties of the mapping $\Phi_\xi$, which associates to every L\'evy process $\eta$ the distribution of the corresponding exponential functional for a fixed $\xi$, independent of $\eta$. While the case of $\xi_t = t$ is well studied and gives rise to all self-decomposable distributions, much less is known for general $\xi$.

**Monday**, 24^{th} November 2014,16:30, LMU, room B 251, Theresienstr. 39, Munich

Benedikt Stufler (LMU, Mathematisches Institut der Universität München)

Title: Scaling Limits of Random Graphs from Subcritical Classes.

Abstract: Click here.

**Monday**, 24^{th} November 2014

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 1^{st} December 2014,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Daniel Stilck Franca (TUM)

Title: Log-Sobolev Inequalities for (Quantum)-Markov Chains.

Abstract: We explain how to derive mixing time bounds for quantum Markov chains and entropic inequalities relevant for quantum information theory through log-Sobolev inequalities, focusing on the doubly-stochastic case. We show how to compute log-Sobolev constants by embedding classical Markov chains in the quantum chain and compute the log-Sobolev-1 constant for the random walk on the complete graph.

**Tuesday**, 2^{nd} December 2014,16:15, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Prof. Olimjon Sharipov (Institute of Mathematics, National University

of Uzbekistan, Tashkent, Uzbekistan)

Title: Bootstrap for dependent Hilbert space-valued random variables

and its application.

Abstract: We will give the results on consistency of the bootstrap for the sample mean of the dependent Hilbert spaces-valued observations. Namely we will consider near epoch dependent observations. Sequential bootstrap will be discussed as well. Applications to von Mises statistics and change point detection will be given.

The talk is based on joint works with H. Dehling, M. Wendler, J. Tewes.

**Monday**, 8^{th} December 2014,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Dr. Renato Soares dos Santos (WIAS Berlin)

Title: Quenched CLT for ballistic random walks in non-uniformly elliptic random environments.

Abstract: Quenched CLTs have been recently proven for large classes of ballistic random walks in random environments under assumptions of large finite moments of the regeneration time. We will discuss an extension of these results when the regeneration time has only slightly more than a second moment, but additionally Sznitman's $(T)_\gamma$ condition holds. This extension is only relevant in the non-uniformly elliptic case. Joint work with Élodie Bouchet and Christophe Sabot.

**Monday**, 15^{th} December 2014,16:30, LMU, room B 251, Theresienstr. 39, Munich

Prof. Rob van den Berg (Vrije Universiteit Amsterdam)

Title: Frozen percolation

Abstract: Motivated by phenomena related to sol-gel transitions, D. Aldous (2000) introduced and analysed a percolation model on a tree where infinite clusters are `frozen'. Soon after his work, Benjamini and Schramm pointed out that such a process does not exist on the square lattice (and other planar lattices).

**Monday**, 12^{th} January 2015,16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Franz Rembart (University of Oxford)

Title: Branch merging on continuum trees with applications to regenerative tree growth.

Abstract: We introduce the $(\alpha, \theta)$-model as an example of a regenerative tree growth process with leaf labels. We explore its connection to a natural ordered extension of the two-parameter Chinese restaurant process as introduced recently by Pitman and Winkel, and study its asymptotic behavior. The delabelled trees have a binary continuum fragmentation tree as their distributional scaling limit, giving rise to the leaf label embedding problem. We address this problem by using branch merging on continuum trees. This is a new operation on trees, even in the special case of the Brownian CRT, which arises as scaling limit for $\alpha=1/2$ and $\theta=1/2$ or $\theta=3/2$. We further use branch merging to define a new tree-valued Markov process which has the distribution induced by the Brownian CRT as a stationary distribution. This talk is based on http://arxiv.org/pdf/1412.7766.pdf.

**Thursday**, 15^{th} January 2015

Stochastic Differential Equations Day

**Monday**, 19^{th} January 2015, 15:00 and 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)

Lorenzo Taggi (Max-Planck-Institut Leipzig)

Title: Critical density of activated random walk.

Abstract: We consider a system with two types of particles, A (active) and S (sleeping), on the d-dimensional lattice. The system is governed by the following rules. Particles of type A perform independent, continuous time simple random walk until they turn into S-particles. This happens at a rate lambda. Particles of type S do not move. Whenever two or more particles share a site they all turn into A-type immediately. The system exhibits a transition from a local-fixation phase to an active phase. We discuss how the critical density separating the two phases depends on the parameters of the model. In particular, we show that in presence of a bias the system sustains activity even for particle density below the unit and we discuss how the bias affects the critical density.

Alberto Chiarini (TU Berlin)

Title: (Local) CLT for symmetric Diffusions in a degenerate Random Environment.

Abstract: We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. The diffusion is formally associated with $L^\omega u = \nabla\cdot(a^\omega\nabla u)$. We prove for $X$ a quenched (local) central limit theorem, under some moment conditions on the environment; the key tools are the sublinearity of the corrector and a parabolic Harnack's inequality both obtained using the celebrated Moser's iteration technique.

**Monday**, 19^{th} January 2015

Graduate Seminar Financial- and Actuarial Mathematics LMU and TUM

**Monday**, 26^{th} January 2015,15:00, TUM, lecture hall 2.02.01, Parkring 11, Garching-Hochbrück (Technische Universität München)

Dr. Julien Sohier (Technische Universiteit Eindhoven)

Title: Conditioned, quasi-stationary, restricted measures and escape from metastable states

Abstract: We study the asymptotic hitting time \tau_n of a family of Markov processes X_n to a target set G_n when the process starts from a trap defined by general properties. We give an explicit description of the law of X_n conditioned to stay within the trap, and from this we deduce the exponential distribution of \tau_n . Our approach is very broad —it does not require reversibility, the target G_n does not need to be a rare event, and the traps and the limit on n can be of very general nature— and leads to explicit bounds on the deviations of \tau_n from exponentially. We provide two non trivial examples to which our techniques directly apply. This is joint work with R. Fernandez, F. Manzo, F.R. Nardi and E. Scoppola.

**Monday**, 26^{th} January 2015,16:30, TUM, lecture hall 2.02.01, Parkring 11, Garching-Hochbrück (Technische Universität München)

Prof. Dr. Alessandra Faggionato (Universita di Roma , Italy)

Title: Mixing time and local exponential ergodicity of the East-like process on Z^d

Abstract:The East-like process on Z^d is a kinetically constrained model, supposed to catch some of the main features of the complex dynamics of fragile glasses. Particles on Z^d performs a stochastic Glauber-type dynamics, where a spin flip at site x is allowed only if a suitable constraint concerning the local configuration around x is satisfied. In this talk we concentrate on the out-of-equilibrium dynamics discussing a form of local exponential ergodicity and the behavior of the mixing time in finite boxes. Joint work with F. Martinelli and P. Chleboun.

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