Asymptotics for the number of walks in a Weyl chamber of type B

ABSTRACT We consider lattice walks in ℝk confined to the region 0<x1<x2…<xk with 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 n...

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Bibliographic Details
Published inRandom structures & algorithms Vol. 45; no. 2; pp. 261 - 305
Main Author Feierl, Thomas
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.09.2014
Wiley Subscription Services, Inc
Subjects
Algorithms
Asymptotic properties
asymptotics
Chambers
determinants
Infinity
lattice walks
Lattices
Mathematical models
Reflection
saddle point method
Walls
Weyl chamber
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ISSN1042-9832
1098-2418
1098-2418
DOI10.1002/rsa.20467

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Summary:ABSTRACT We consider lattice walks in ℝk confined to the region 0<x1<x2…<xk with 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
Bibliography:ark:/67375/WNG-1T85839S-8
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ArticleID:RSA20467
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ISSN:1042-9832
1098-2418
1098-2418
DOI:10.1002/rsa.20467