We examine the distributions of non-commutative polynomials of non-atomic, freely independent random variables. In particular, we obtain an analogue of the Strong Atiyah Conjecture for free groups, ...

Let P = (pjk) be the transition matrix of an ergodic, finite Markov chain with no cyclically moving sub-classes. For each possible transition (j, k), let Hjk(x) be a distribution function admitting a ...

This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or, more specifically, subexponential random variables. A key application of this ...