RANDOM WALKS DRIVEN BY LOW MOMENT MEASURES

作者：Bendikov Alexander^*; Saloff Coste Laurent

来源：Annals of Probability, 2012, 40(6): 2539-2588.

DOI：10.1214/11-AOP687

• Random walk
• group invariants
• moments

We study the decay of convolution powers of probability measures without second moment but satisfying some weaker finite moment condition. For any locally compact unimodular group G and any positive function rho : G --> [0, +infinity], we introduce a function Phi(G,rho) which describes the fastest possible decay of n bar right arrow phi((2n)) (e) when phi is a symmetric continuous probability density such that integral rho phi is finite. We estimate Phi(G,rho) for a variety of groups G and functions rho. When rho is of the form rho = rho o delta with rho : [0, +infinity) --> [0, +infinity), a fixed increasing function, and delta : G --> [0, +infinity), a natural word length measuring the distance to the identity element in G, Phi(G,rho) can be thought of as a group invariant.

• 出版日期2012-11