作者：Collevecchio, Andrea; Schmitz, Tom
作者单位：Universita Ca Foscari Venezia; Max Planck Society
摘要：We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [Probab. Theory Relate...
作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and fluctuations of near-geodesics in the network generated by the line process. The notion of a Poissonian city is introduced, in which connections between pairs of nodes are made using simple no-overshoot paths based on the Poisson line process. Asymptotics for geom...
