报告人简介：向开南，南开大学数学科学学院教授、博士生导师
报告摘要：The uniform spanning forest measure
on the Euclidian lattice
is not necessarily concentrated on the set of spanning trees of. In fact, a remarkable result of R. Pemantle (1991) says that is concentrated on spanning trees if and only if
. We study the
-biased random walk on with
and
, and prove that the corresponding is of finitely many trees if and only if
. More precisely, we prove that the uniform spanning forest associated with the biased random walk on has
trees if and infinitely many trees if. Our method relies on analyzing the spectral radius and the speed of the biased random walk. When d=1 and, the related free uniform spanning forest is the singleton of the tree
, whereas the related wired uniform spanning forest has two trees. The talk is based on a joint work with Zhan Shi (Paris VI Univ.), Vladas Sidoravicius (NYU-Shanghai), He Song (Taizhou Univ.) and Longmin Wang (Nankai Univ.).
报告主持：闫理坦
