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A product formula for the TASEP on a ring
Author(s) -
Aas Erik,
Sjöstrand Jonas
Publication year - 2016
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20595
Subject(s) - mathematics , combinatorics , permutation (music) , ring (chemistry) , order (exchange) , product (mathematics) , random permutation , conjecture , queue , stationary distribution , shuffling , interpretation (philosophy) , distribution (mathematics) , discrete mathematics , computer science , markov chain , statistics , symmetric group , physics , mathematical analysis , chemistry , geometry , organic chemistry , finance , acoustics , economics , programming language
For a random permutation sampled from the stationary distribution of the TASEP on a ring, we show that, conditioned on the event that the first entries are strictly larger than the last entries, the order of the first entries is independent of the order of the last entries. The proof uses multi‐line queues as defined by Ferrari and Martin, and the theorem has an enumerative combinatorial interpretation in that setting. Finally, we present a conjecture for the case where the small and large entries are not separated. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 247–259, 2016