DOAJ
Open Access
2012
A phase transition in the distribution of the length of integer partitions
Dimbinaina Ralaivaosaona
Abstrak
We 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 Erdős and Lehner published in 1941 that the distributions of the length in random restricted $(d=2)$ and random unrestricted $(d \geq n+1)$ 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.
Topik & Kata Kunci
Penulis (1)
D
Dimbinaina Ralaivaosaona
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2012
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2999
- Akses
- Open Access ✓