Uniform spanning forests on biased Z^d


主题:   Uniform spanning forests on biased Z^d主讲人:   向开南 教授地点:   松江校区2号学院楼331理学院报告厅时间:   2018-03-16 15:00:00组织单位:   理学院


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.).





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