Products Of Random Variables: Applications To Problems Of Physics and To Arithmetical Functions

Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variables and obtaining results with dependent variables using a new Bonferroni-type argument.

Systematically and comprehensively tracks the progression of research completed in the area over the last twenty years.

Well-indexed and well-referenced, Products of Random Variables

Clarifies foundational concepts such as symmetric and limiting distributions of products

Examines various limit theorems, from logarithmically Poisson distributions to triangular arrays

Explores characterization theorems, detailing normal, Cauchy, and bivariate distributions

Describes models of interactive particles

Elucidates dual systems of interactive particles, dual systems of increasing size, and random walks

Covers the Kubilius-Turán inequality and distributions for multiplicative functions

Probes sequences of prime divisors and prime numbers

Discusses Markov chains, Hilbert spaces, and quotients of random variables

Presents income growth models and numerous other applied models tapping products of random variables

Authored by eminent scholars in the field, this volume is an important research reference for applied mathematicians, statisticians, physicists, and graduate students in these disciplines.