Abstract for the talk at 07.05.2013 (16:45 h)

Oberseminar ANALYSIS - PROBABILITY

Yinshan Chang (Université Paris-Sud)
Loop covering probabilities

Given a sequence of undirected connected graphs Gn of n vertices with bounded degrees and weights and an additional sequence of killing parameters cn, one can define a sequence μn of natural non-normalized measures on non-trivial loops of Gn. Denote by Qn the transition matrix associated with Gn. Assuming that the empirical distributions νn of the eigenvalues of Qn converge, we determine the limit of the μn-proportion of {loops which cover every vertex} as n →∞. Let Ln be the Poissonian “loop soup” with intensity μn-  n. A a corollary, we determine the limit law of the number of the loops covering the whole graph. As two concrete examples, we consider the closed balls in a regular graph and the discrete tori.

 

01.03.2017, 13:57