2011/03/08 by Alexander Gnedin, Grigori Olshanski
Mathematics · #math.PR #math.CO
published as Advances in Applied Mathematics 48 (2012), no. 5, 615-639 · 29 pages, Latex
arxiv created 2011/03/08 · arxiv updated 2013/03/04
We introduce a probability distribution Q on the group of permutations of the set Z of integers. Distribution Q is a natural extension of the Mallows distribution on the finite symmetric group. A one-sided infinite counterpart of Q, supported by the group of permutations of the set N of natural numbers, was studied previously in our paper [Gnedin and Olshanski, Ann. Prob. 38 (2010), 2103-2135; arXiv:0907.3275]. We analyze various features of Q such as its symmetries, the support, and the marginal distributions.