The two-sided infinite extension of the Mallows model for random permutations

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.