Record‐dependent measures on the symmetric groups
Copyright policy )Record‐dependent measures on the symmetric groups
A probability measure Pn on the symmetric group is said to be record‐dependent if depends only on the set of records of a permutation . A sequence of consistent record‐dependent measures determines a random order on ℕ. In this paper we describe the extreme elements of the convex set of such P. This problem turns out to be related to the study of asymptotic behavior of permutation‐valued growth processes, to random extensions of partial orders, and to the measures on the Young‐Fibonacci lattice. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 2014 © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46,688–706, 2015
- Massachusetts Institute of Technology United States
- Queen Mary University of London United Kingdom
- Institute for Information Transmission Problems Russian Federation
Permutations, words, matrices, Martin boundary, random permutation, Probability (math.PR), record, Boundary theory for Markov processes, Probabilistic methods in group theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Probability measures on groups or semigroups, Fourier transforms, factorization, Mathematics - Probability
Permutations, words, matrices, Martin boundary, random permutation, Probability (math.PR), record, Boundary theory for Markov processes, Probabilistic methods in group theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Probability measures on groups or semigroups, Fourier transforms, factorization, Mathematics - Probability
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