作者：Blachere, Sebastien; Haissinsky, Peter; Mathieu, Pierre
作者单位：Aix-Marseille Universite
摘要：We study asymptotic proper-ties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91-112]), we give an alternative proof relying...
作者：Adamczak, Radoslaw; Latala, Rafal
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; University of Warsaw
摘要：We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for canonical U-statistics of arbitrary order d, extending the previously known results for d = 2. The nasc's are expressed as growth conditions on a parameterized family of norms associated with the U-statistics kernel.
