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 (1)

• Spatial random permutations and infinite cycles

Cited by in corpus (10)

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• 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