Let Γ be a nonelementary hyperbolic group with word metric d and ∂Γ its boundary equipped visual for some parameter > 1 . Fix superexponential symmetric probability μ on whose support generates as semigroup, denote by ρ the spectral radius of random walk Y step distribution μ. ν 1,2,3 , … mean λ = ∑ k ∞ kν < BRW branching offspring base motion let H volume growth rate trace We prove ∈ − that Ha...

Abstract The study of multivariate extremes is dominated by regular variation, although it well known that this approach does not provide adequate distinction between random vectors whose components are always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden variation conditional extreme value model. Thes...

We consider non-bijective piecewise rotations of the plane. These maps belong to a family introduced in previous papers by Boshernitzan and Goetz. derive this paper some upper bounds size limit set. This improves results [M. A. Goetz, A dichotomy for two-parameter rotation, Ergodic Theory Dynam. Syst. 23(3) (2003), pp. 759–770.].