 

Liviu I. Nicolaescu
Derangements and asymptotics of the Laplace transforms of large powers of a polynomial


Published: 
April 12, 2004 
Keywords: 
derangements, Laplace transforms, asymptotics, multinomial distributions 
Subject: 
44A10, 05A05, 05A10, 05A16, 41A60, 33C45 


Abstract
We use a probabilistic approach to produce sharp asymptotic estimates as
n→∞ for the Laplace transform of P^{n}, where P is a
fixed complex polynomial. As a consequence we obtain a new
elementary proof of a result of AskeyGillisIsmailOfferRashed
in the combinatorial theory of derangements.


Acknowledgements
This work was partially suported by the NSF grant DMS0303601.


Author information
Dept. of Mathematics, University of Notre Dame, Notre Dame, IN 465564618
nicolaescu.1@nd.edu
http://www.nd.edu/~lnicolae/

