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, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Katja Miller (TUM)
Monday, 6th November 2017, 16:30, LMU, room B 251, Theresienstr. 39, Munich
Prof Simone Cerreia Vioglio (Universität Bocconi, Mailand)
Monday, 27th November 2017, 16:30, LMU, room B 252, Theresienstr. 39, Munich
Dr. Timo Hirscher (Universitet Stockholm)
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, 15th January 2017, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Dr. Christian Mönch (Universität Mannheim)
How to get to Garching-Hochbrück