2012/02/16 by Alexander Gnedin, Vadim Gorin, Gnedin, Alexander +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR
paper · pdf · doi:10.48550/arxiv.1202.3680
23 pages. v2: minor corrections, to appear in Random Structures and Algorithms
openalex publication_date 2012/02/16 · arxiv created 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
A probability measure Pn on the symmetric group \mathfrak Sn is said to be record-dependent if Pn(σ) depends only on the set of records of a permutation σ∈\mathfrak Sn. A sequence P=(Pn)_n∈\mathbb N of consistent record-dependent measures determines a random order on \mathbb 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.