Record-dependent measures on the symmetric groups
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1202.3680.pdf
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Author(s)
Gnedin, Alexander
Gorin, Vadim
Date Issued
March 2014
Journal
Random Structures & Algorithms
Publisher
Wiley Blackwell
Citation
Gnedin, Alexander and Vadim Gorin. “Record-Dependent Measures on the Symmetric Groups.” Random Structures & Algorithms 46, 4 (March 2014): 688–706 © 2014 Wiley Periodicals, Inc
Version
Author's final manuscript
Abstract
A probability measure P[subscript n] on the symmetric group S[subscript n] is said to be record-dependent if P[subscript n]( σ ) depends only on the set of records of a permutation σ ∈ S[subscript n]. A sequence P = ( P n )[subscript n ∈ N] 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1002/RSA.20526
