Random partitions with restricted part sizes

: ForasubsetS ofpositiveintegerslet (n, S)bethesetofpartitionsofnintosummands that are elements of S. For every (n, S), let Mn() be the number of parts, with multiplicity, that has. Put a uniform probability distribution on (n, S), and regard Mn as a random variable. In this paper the limiting density of the (suitably normalized) random variable Mn is determined for sets that are sufficiently regular. In particular, our results cover the case S = {Q(k) : k 1}, where Q(x) is a fixed polynomial of degree d 2. For specific choices of Q, the limiting density has appeared before in rather different contexts such as Kingman's coalescent, and processes associated with the maxima of Brownian bridge and Brownian meander processes.

• Type: Journal
• Year: 2008
• Where: RSA
• Authors: William M. Y. Goh, Pawel Hitczenko
• Keywords: Random Variable, Random Variable Mn, RSA 2008, Uniform Probability Distribution