Random permutations with cycle weights

Abstract

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a fraction of $n$ or a logarithmic power of $n$.

Published in at http://dx.doi.org/10.1214/10-AAP697 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Spatial random permutations and infinite cycles
• Critical Temperature of Dilute Bose Gases
• Cycles of random permutations with restricted cycle lengths

Cited by in corpus (24)

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• Random partitions in statistical mechanics
• The limit shape of random permutations with polynomially growing cycle weights
• Macroscopic loops in the Bose gas, Spin O(N) and related models
• Large cycles and a functional central limit theorem for generalized weighted random permutations
• A new approach to the characteristic polynomial of a random unitary matrix
• Central limit theorem for multiplicative class functions on the symmetric group
• Shift in critical temperature for random spatial permutations with cycle weights
• Multiplicative arithmetic functions and the generalized Ewens measure
• Limit shapes for Gibbs partitions of sets
• The generalized weighted probability measure on the symmetric group and the asymptotic behavior of the cycles
• On statistics of permutations chosen from the Ewens distribution
• Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula
• A geometric approach to conjugation-invariant random permutations
• Birth-and-death Polya urns and stationary random partitions
• Infinite cycles of interacting bosons
• The order of large random permutations with cycle weights
• Emergence of condensation in Kingman's model of selection and mutation
• Universality of Asymptotically Ewens Measures on Partitions
• Simultaneous occurrence of off-diagonal long-range order and infinite permutation cycles in systems of interacting atoms