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 A110899 Number of different stationary distributions of a certain random walk whose states are permutations of 1,...,n. The transitions depend on two sorted vectors x and z. The state sigma goes to rank((z[sigma]-x)[rperm] +x), where rperm is a random (uniform) permutation. If x and z are realizations of independent random variables X and Z and pi is a permutation drawn from the stationary distribution, the vector z[pi]-x is a realization of a random variable Y where Z ~ X+Y. 0

%I #10 Nov 05 2013 20:59:40

%S 0,1,2,208

%N Number of different stationary distributions of a certain random walk whose states are permutations of 1,...,n. The transitions depend on two sorted vectors x and z. The state sigma goes to rank((z[sigma]-x)[rperm] +x), where rperm is a random (uniform) permutation. If x and z are realizations of independent random variables X and Z and pi is a permutation drawn from the stationary distribution, the vector z[pi]-x is a realization of a random variable Y where Z ~ X+Y.

%H C. L. Mallows, <a href="http://arXiv.org/abs/0708.1051">Deconvolution by simulation</a>, arXiv:0708.1051 [stat.CO].

%H C. L. Mallows, <a href="http://www.ams.org/mathscinet-getitem?mr=2459175">Deconvolution by simulation</a>

%e If n=2, the transition matrix is one of (0.5, 0.5), (1, 0.5), (0.5, 0.5), or (0, 0.5). The stationary distributions are (0.5, 0.5) and (1, 0).

%K hard,nonn,more

%O 0,3

%A _Colin Mallows_, Sep 20 2005

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