Integration of direct limits of real random variables

on direct sums of baer modules

the notion of baer modules was defined recently

On the Ratio of Rice Random Variables

 The ratio of independent random variables arises in many applied problems. In this article, the distribution of the ratio X/Y is studied, when X and Y are independent Rice random variables. Ratios of such random variable have extensive applications in the analysis of noises of communication systems. The exact forms of probability density function (PDF), cumulative distribution function (CDF) a...

Generalized Covering Groups and Direct Limits

Limits Laws for Geometric Means of Free Random Variables

Let {Tk}k=1 be a family of ∗–free identically distributed operators in a finite von Neumann algebra. In this work we prove a multiplicative version of the free central limit Theorem. More precisely, let Bn = T ∗ 1 T ∗ 2 . . . T ∗ nTn . . . T2T1 then Bn is a positive operator and B 1/2n n converges in distribution to an operator Λ. We completely determine the probability distribution ν of Λ from...

Limits Laws for Geometric Means of Free Positive Random Variables

Let {ak}k=1 be free identically distributed positive non–commuting random variables with probability measure distribution μ. In this paper we proved a multiplicative version of the Free Central Limit Theorem. More precisely, let bn = a 1/2 1 a 1/2 2 . . . an . . . a 1/2 2 a 1/2 1 then bn is a positive operator with the same moments as xn = a1a2 . . . an and b 1/2n n converges in distribution to...