Multidimensional large deviation local limit theorems

Large deviations of combinatorial distributions II: Local limit theorems

This paper is a sequel to our paper [17] where we derived a general central limit theorem for probabilities of large deviations1 applicable to many classes of combinatorial structures and arithmetic functions; we consider corresponding local limit theorems in this paper. More precisely, given a sequence of integral random variables {Ωn}n≥1 each of maximal span 1 (see below for definition), we a...

Limit Theorems for Multidimensional Markov Processes

An informal exposition of some recent results and conjectures. A multidimensional Markov process (mdmp) is a dynamical system (K, m, T) where: K space of the sequences of symbols from a finite alphabet / = (α, fo,... z) indexed by the elements η e Z = lattice formed by the d-ples of integers. K is regarded as K = TίηeZd I i.e. as a product space of copies of/; furthermore / is topologized by th...

Local Limit Theorems for Free

Almost sure local limit theorems

Chung and Erdös (1951) are among the first to prove some form of an almost sure local limit theorem (cf. Csáki et al., 1993). Here we propose a formulation of such statements and discuss related problems. Surely, Frits will enjoy them. c ©2001, June 19.

Local Limit Theorems for Free Groups

In this paper we obtain a local limit theorem for elements of a free group G under the abelianization map [·] : G → G/[G, G]. This is obtained via an analysis involving subshifts of finite type, where we obtain a result of independent interest. The case of fundamental groups of compact surfaces of genus ≥ 2 is also discussed. 0. Introduction Let G denote the free group on k ≥ 2 generators {a1, ...