Record-dependent measures on the symmetric groups

Details Record-dependent measures on the symmetric groups Record-dependent measures on the symmetric groups

2012-02-16

arxiv.org/abs/1202.3680v1

Mathematics

Probability

24 pages

Scientific paper

Probability measure P_n on the symmetric group S_n is said to be record-dependent if P_n(s) depends only on the set of records of permutation s. A sequence P=(P_n) of consistent record-dependent measures determines a random order on the set of positive integers. 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.

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