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Journal article
Random partitions with restricted part sizes
Random structures & algorithms, v 32(4), pp 440-462
Jul 2008
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Abstract
For a subset $\cal{S}$ of positive integers let Ω(n,$\cal{S}$) be the set of partitions of n into summands that are elements of $\cal{S}$. For every λ ∈ Ω(n,$\cal{S}$), let Mn(λ) be the number of parts, with multiplicity, that λ has. Put a uniform probability distribution on Ω(n,$\cal{S}$), 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 $\cal{S}$ = {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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008
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Details
- Title
- Random partitions with restricted part sizes
- Creators
- William M.Y GohPawel Hitczenko
- Publication Details
- Random structures & algorithms, v 32(4), pp 440-462
- Publisher
- Wiley Subscription Services, Inc., A Wiley Company; Hoboken
- Number of pages
- 23
- Grant note
- NSA (H98230‐05‐1‐0016)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]; Mathematics
- Web of Science ID
- WOS:000256925300002
- Scopus ID
- 2-s2.0-52649177729
- Other Identifier
- 991014878036704721
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- Web of Science research areas
- Computer Science, Software Engineering
- Mathematics
- Mathematics, Applied