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

Advances in Applied Mathematics. 2012. Vol. 48. No. 5. P. 615-639.
Gnedin A., Olshanski G.

We introduce a probability distribution Q on the infinite group S_Z of permutations of the set of integers Z. The 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 N, was studied previously in our paper [A. Gnedin, G. Olshanski, q-Exchangeability via quasi-invariance, Ann. Probab. 38 (2010) 2103–2135, arXiv:0907.3275]. We analyze various features of Q such as its symmetries, the support, and the marginal distributions.