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Pattern‐avoiding permutations and Brownian excursion part I: Shapes and fluctuations
Author(s) -
Hoffman Christopher,
Rizzolo Douglas,
Slivken Erik
Publication year - 2017
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.20677
Subject(s) - excursion , brownian excursion , brownian motion , permutation (music) , mathematics , connection (principal bundle) , random permutation , scaling , statistical physics , combinatorics , scaling limit , computer science , geometric brownian motion , physics , diffusion process , geometry , statistics , knowledge management , innovation diffusion , political science , acoustics , law , block (permutation group theory)
Permutations that avoid given patterns are among the most classical objects in combinatorics and have strong connections to many fields of mathematics, computer science and biology. In this paper we study the scaling limits of a random permutation avoiding a pattern of length 3 and their relations to Brownian excursion. Exploring this connection to Brownian excursion allows us to strengthen the recent results of Madras and Pehlivan [25] and Miner and Pak [29] as well as to understand many of the interesting phenomena that had previously gone unexplained. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 394–419, 2017