Ph. Dumas Algorithms Project, INRIA Rocquencourt BP 105, 78153 Le Chesnay Cedex, France
L. Thimonier Laboratoire de Mathématiques et d'Informatique Fondamentale, Université de Picardie, 80039 Amiens Cedex, France

Random palindromes:
multivariate generating function
and Bernoulli density

Consider a finite alphabet with a probability distribution p. We study the probability $\delta(p)$ of obtaining a palindrome in a finite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed form expression for $\delta(p)$.Moreover we describe completely the cases where $\delta(p)$ has value less than 1, in connection with the singularities of the generating function. Except for the case of a one or two letters alphabet it is found that $\delta(p)$ is always less than 1.