Cycle structure of random permutations with cycle weights

Abstract

We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the parameters, while the distributions of finite cycles are usually independent Poisson random variables.

22 pages, 2 figures

References in corpus (3)

• Spatial random permutations and infinite cycles
• Random permutations with cycle weights
• Spatial random permutations with small cycle weights

Cited by in corpus (10)

• On the number of cycles in a random permutation
• Asymptotic statistics of cycles in surrogate-spatial permutations
• Random permutation matrices under the generalized Ewens measure
• Monotonous subsequences and the descent process of invariant random permutations
• The Characteristic Polynomial of a Random Permutation Matrix at Different Points
• Multiplicative arithmetic functions and the generalized Ewens measure
• Limit shapes for Gibbs partitions of sets
• Short cycles of random permutations with cycle weights: point processes approach
• On the Golomb-Dickman constant under Ewens sampling
• A geometric approach to conjugation-invariant random permutations