Combinatorics of geometrically distributed random variables: Length of ascending runs

Abstract

For n independently distributed geometric random variables we consider the average length of the m-th run, for fixed m and n → ∞. One particular result is that this parameter approaches 1 + q. In the limiting case q → 1 we thus rederive known results about runs in permutations. © Springer-Verlag Berlin Heidelberg 2000.