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Asymptotics for the number of walks in a Weyl chamber of type B
Author(s) -
Feierl Thomas
Publication year - 2014
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.20467
Subject(s) - random walk , mathematics , infinity , class (philosophy) , lattice (music) , type (biology) , quantum walk , combinatorics , reflection (computer programming) , mathematical analysis , physics , quantum mechanics , computer science , statistics , ecology , artificial intelligence , acoustics , quantum algorithm , quantum , biology , programming language
We consider lattice walks inℝ kconfined to the region 0 < x 1 < x 2 … < x kwith fixed (but arbitrary) starting and end points. These walks are assumed to be such that their number can be counted using a reflection principle argument. The main results are asymptotic formulas for the total number of walks of length n with either a fixed or a free end point for a general class of walks as n tends to infinity. As applications, we find the asymptotics for the number of k ‐non‐crossing tangled diagrams as well as asymptotics for two k ‐vicious walkers models subject to a wall restriction. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 45, 261–305, 2014