Local limit theorems in free probability theory

Limit Theorems in Free Probability Theory. Ii

Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line R+ and on the unit circle T we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.

Fe b 20 06 LIMIT THEOREMS IN FREE PROBABILITY THEORY

Based on a new analytical approach to the definition of additive free con-volution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical Probability Theory.

Local Limit Theorems for Free

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, ...

Limit theorems of probability theory : Sequences of independent random variables

The simple notion of statistical independence lies at the core of much that is important in probability theory. First there was the classical central limit theorem (CLT) of De Moivre and Laplace which, in its final form due to Paul Lévy, says that the sum Sn of n independent and identically distributed (i.i.d.) random variables Xj (1 ≤ j ≤ n) having finite second moments is asymptotically Gauss...