Random permutations without macroscopic cycles

Betz, Volker and Schäfer, Helge and Zeindler, Dirk (2019) Random permutations without macroscopic cycles. Annals of Applied Probability. ISSN 1050-5164 (In Press)

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Abstract

We consider uniform random permutations of length n conditioned to have no cycle longer than nβ with 0 < β < 1, in the limit of large n. Since in unconstrained uniform random permutations most of the indices are in cycles of macroscopic length, this is a singular conditioning in the limit. Nevertheless, we obtain a fairly complete picture about the cycle number distribution at various lengths. Depending on the scale at which cycle numbers are studied, our results include Poisson convergence, a central limit theorem, a shape theorem and two different functional central limit theorems.

Item Type:
Journal Article
Journal or Publication Title:
Annals of Applied Probability
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1804
Subjects:
ID Code:
137392
Deposited By:
Deposited On:
07 Oct 2019 10:40
Refereed?:
Yes
Published?:
In Press
Last Modified:
29 Feb 2020 07:15