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.
Publié le : 2011-02-15
Classification:
Random permutations,
cycle weights,
cycle lengths,
Ewens distribution,
60K35
@article{1292598036,
author = {Betz, Volker and Ueltschi, Daniel and Velenik, Yvan},
title = {Random permutations with cycle weights},
journal = {Ann. Appl. Probab.},
volume = {21},
number = {1},
year = {2011},
pages = { 312-331},
language = {en},
url = {http://dml.mathdoc.fr/item/1292598036}
}
Betz, Volker; Ueltschi, Daniel; Velenik, Yvan. Random permutations with cycle weights. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp. 312-331. http://gdmltest.u-ga.fr/item/1292598036/