A Phase transition in the distribution of the length of integer partitions

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dc.creatorRalaivaosaonay, Dimbinaina
dc.date05/24/2013
dc.dateFri, 24 May 2013
dc.dateFri, 24 May 2013 11:39:39
dc.dateFri, 24 May 2013 11:39:39
dc.date.accessioned2015-03-18T11:28:59Z
dc.date.available2015-03-18T11:28:59Z
dc.descriptionPaper presented at Strathmore International Math Research Conference on July 23 - 27, 2012
dc.descriptionWe assign a uniform probability to the set consisting of partitions of a positive integer n such that the multiplicity of each summand is less than a given number d and we study the limiting distribution of the number of summands in a random partition. It is known from a result by Erd˝os and Lehner published in 1941 that the distributions of the length in random restricted (d = 2) and random unrestricted (d n + 1) partitions behave very differently. In this paper we show that as the bound d increases we observe a phase transition in which the distribution goes from the Gaussian distribution of the restricted case to the Gumbel distribution of the unrestricted case.
dc.description.abstractWe assign a uniform probability to the set consisting of partitions of a positive integer n such that the multiplicity of each summand is less than a given number d and we study the limiting distribution of the number of summands in a random partition. It is known from a result by Erd˝os and Lehner published in 1941 that the distributions of the length in random restricted (d = 2) and random unrestricted (d n + 1) partitions behave very differently. In this paper we show that as the bound d increases we observe a phase transition in which the distribution goes from the Gaussian distribution of the restricted case to the Gumbel distribution of the unrestricted case.
dc.formatNumber of Pages:18 p.
dc.identifier.urihttp://hdl.handle.net/11071/3581
dc.languageeng
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dc.subjectAsymptotic expansions
dc.subjectInteger partitions
dc.subjectMultiplicities
dc.subjectLimit distribution
dc.titleA Phase transition in the distribution of the length of integer partitions
dc.typeConference Paper
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