Derangements and asymptotics of Laplace transforms of polynomials

Abstract

We use a probabilistic approach to describe the behavior as $n->\infty$ of the Laplace transforms of $P^n$, where $P$ a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer in the combinatorial theory of derangements.

15 pages, LaTeX