Oberseminar Wahrscheinlichkeitstheorie und andere Vorträge im Wintersemester 2017/18
Monday, 18th September 2017, 15:30, LMU, room B 252, Theresienstr. 39, Munich
Andrea Schmidbauer (LMU)
Title: Site percolation in high dimensions
Abstract: Percolation usually studies the random sub-lattice consisting of occupied bonds. In contrast to the majority of the literature, we study site percolation and restrict attention to the hypercubic lattice Zd, where each site is occupied with probability p 2 [0; 1]. A key result in high-dimensional percolation is the so-called infrared bound that has been proven by Hara and Slade in 1990 for bond percolation. The aim of this presentation is to explain how the infrared bound can be proven for site percolation. The proof makes use of a combinatorial expansion technique, the so-called percolation lace-expansion. Our lace-expansion analysis covers the nearest-neighbor model.
Monday, 18th September 2017, 16:30, LMU, room B 252, Theresienstr. 39, Munich
Leonid Kolesnikov (LMU)
Title: The critical 1-arm exponent for the Ising model on Cayley trees
Abstract: The ferromagnetic Ising model is one of the most extensively studied models from statistical mechanics. Here, we consider a regular tree as the underlying graph. We consider subtrees of depth n with fixed plus-valued boundary spins and investigate the expected spin value of the root of the tree with respect to the Gibbs measure on the subtree. It is well known that in the absence of an external field, the model undergoes a phase transition. At critical temperature, the influence of a plus boundary condition fades away when we take the limit in the distance between the root and the boundary of the subtree, i.e. the expected root spin is converging towards zero for n to infinity. Our main goal is to quantify the rate of this convergence.
A short introduction to the Ising model will be given at the beginning of the talk.
Monday, 23rd October 2017, 14:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Katja Miller (TUM)
Title: Random walks on oriented percolation and in recurrent random environments
Wednesday, 25th October 2017, 1315, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Ercan Sönmez (Heinrich-Heine-Universität, Düsseldorf)
Title: Hausdorff dimension of multivariate operator-self-similar random fields
Abstract: The notion of Hausdorff dimension has been introduced in order to characterize sets which do possess a fractional pattern, commonly referred to as fractals. A typical feature of fractals is that they exhibit reappearing patterns, i.e. many fine details of the set resemble the whole set, a phenomenon which is called self- similarity. In case of multivariate self-similar random fields self-similarity means that a time-scaling corresponds statistically to a scaling in the state space, where the scaling relation is with respect to suitable matrices. This talk provides the first results on the sample paths and fractal dimensions of such fields, including quite general scaling matrices. A short introduction to the notion of Hausdorff dimension will also be given.
Thursday, 2th November 2017, 14:30,TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Stein Andreas Bethuelsen (TUM)
Title: On the projection of the two-dimensional Ising model onto a line
Abstract: Consider the plus-phase of the two-dimensional Ising model below the critical temperature. Schonmann (1988) proved that the projection of this measure onto a line is not a Gibbs measure. In this talk I will review this result, as well as some more recent advances, and discuss some open questions related to Schonmanns work. In particular, I will focus on the following question: is the projection considered by Schonmann one-sided Gibbs? (in order words, is it a g-measure?) Based on joint work with Diana Conache (TUM).
Monday, 6th November 2017, 16:30, LMU, room B 251, Theresienstr. 39, Munich
Prof Simone Cerreia Vioglio (Universität Bocconi, Mailand)
Title: Choquet Integration of Self-adjoint Operators
Abstract: Comonotonicity and comonotonic additivity are at the base of the theory of Choquet integration which has many applications in Economics and Statistics. The main contribution of this work is to propose a definition of comonotonicity for elements of B(H), i.e. bounded self-adjoint operators defined over a complex Hilbert space H. We show that comonotonicity coincides with a form of commutativity. We also de fine the notion of Choquet expectation for elements of B(H): a natural generalization of quantum expectations. We characterize Choquet expectations as the real-valued functionals over B(H) which are comonotonic additive, c-monotone, and normalized.
Monday, 13th November 2017, 16:30,TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Dmitry Zaporozhets, (St. Petersburg Department of Steklov Mathematical Institute, St. Petersburg)
Title: Random convex hulls
Abstract: A basic object of Stochastic geometry is a random convex polytope. We will discuss several models including convex hulls of random walks and Gaussian polytopes.
Monday, 27th November 2017, 16:30, LMU, room B 252, Theresienstr. 39, Munich
Dr. Timo Hirscher (Universität Stockholm)
Title: Consensus formation in the Deffuant model
Abstract: n 2000, Deffuant et al. introduced an interaction scheme to model opinion formation in large groups: Given a network graph and initial opinions, neighbors interact pairwise and either approach a compromise if their disagreement is below a given threshold or ignore each other if not. Concerning the asymptotics of the model, one central question is whether the whole group achieves a general consensus in the long run or splits into irreconcilable parts. We studied this model featuring univariate opinions on integer lattices and infinite percolation clusters as underlying interaction networks. The generalization of the original model to multivariate and measure-valued opinions was analyzed on the simple network given by the doubly-infinite path Z.
Monday, 11th December 2017, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Jan Nagel (Technische Universiteit Eindhoven)
Monday, 18th December 2017, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Caio Teodoro De Magalhaes Alves (Universität Leipzig)
Monday, 15th January 2017, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Christian Mönch (Universität Mannheim)
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