Spring 2015
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: April 10, 2015
Speaker: Chjan C. Lim
Department of Mathematical Sciences,
Rensselaer Polytechnic Institute
Title: "Solutions of Generalized (Ehrenfest’s Dog Flea) Urn Models"
Abstract:
Ehrenfest dog Flea Urn problem reconciled the Arrow of Time in the Second Law with the reversibility of Mechanics. Mark Kac gave the first diagonalization of its Markov transition matrix (by calculating left eigenvectors via generating functions). We provide a related method for solving multi- urn models which leads to a class of linear PDEs for the diagonalizing transformations. We also provide a complete taxonomy of 2-Urn models into solvable, unsolvable, Martingale and non-Martingale and lastly, a class for which a version of the Second Law holds. The last is shown to be equivalent to a probabilistic symmetry condition on the urn models. Appealing examples of the Urn models include the Voter models and the Naming Games, which are well-studied nonequilibrium stochastic models for social opinion dynamics on networks.