Random permutations with cycle weights

Authors
Betz, Volker Ueltschi, Daniel Velenik, Yvan
Citation
Betz, Volker et al., Random permutations with cycle weights, Annals of applied probability , 21(1), 2011, pp. 312-331
Journal title
Annals of applied probability → ACNP
ISSN journal
10505164
Volume
21
Issue
1
Year of publication
2011
Pages
312 - 331
Database
ACNP
SICI code
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.