A Combinatorial and Probabilistic Study of Initial and End Heights of Descents in Samples of Geometrically Distributed Random Variables and in Permutations

Abstract

In words, generated by independent geometrically distributed random variables, we study the lth descent, which is, roughly speaking, the lth occurrence of a neighbouring pair ab with a > b. The value a is called the initial height, and b the end height. We study these two random variables (and some similar ones) by combinatorial and probabilistic tools. (This talk is based on a paper with G. Louchard.)