Vicious walkers, friendly walkers, and young tableaux. III. Between two walls

被引：20

作者：

Krattenthaler, C

Guttmann, AJ

Viennot, XG

机构：

[1] Univ Vienna, Inst Math, A-1090 Vienna, Austria

[2] Univ Melbourne, Dept Math & Stat, Melbourne, Vic 3010, Australia

[3] Univ Bordeaux 1, LaBRI, F-33405 Talence, France

来源：

JOURNAL OF STATISTICAL PHYSICS | 2003年 / 110卷 / 3-6期

关键词：

vicious walkers; friendly walkers; symmetric fuctions; affine Weyl groups;

D O I：

10.1023/A:1022192709833

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We derive exact and asymptotic results for the number of star and watermelon configurations of vicious walkers confined to lie between two impenetrable walls, as well as corresponding results for the analogous problem of infinity-friendly walkers. Our proofs make use of results from symmetric function theory and the theory of basic hypergeometric series.

引用

页码：1069 / 1086

页数：18

共 29 条

[1] Baik J, 2000, COMMUN PUR APPL MATH, V53, P1385, DOI 10.1002/1097-0312(200011)53:11<1385::AID-CPA3>3.0.CO
[2] 2-T
[3] Hexagon model for 3D Lorentzian quantum cosmology
Dittrich, B
Loll, R
[J]. PHYSICAL REVIEW D, 2002, 66 (08):
[4] WALKS, WALLS, WETTING, AND MELTING
FISHER, ME
[J]. JOURNAL OF STATISTICAL PHYSICS, 1984, 34 (5-6) : 667 - 729
[5] EXACT SOLUTION OF THE LOCK STEP MODEL OF VICIOUS WALKERS
FORRESTER, PJ
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (07): : 1259 - 1273
[6] Lattice path proofs for determinantal formulas for symplectic and orthogonal characters
Fulmek, M
Krattenthaler, C
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 77 (01) : 3 - 50
[7] Fulton W., 2004, REPRESENT THEOR, V129
[8] GASPER G, 1990, ENCY MATH ITS APPL, V35
[9] Gessel I. M., 1989, Determinants, paths, and plane partitions
[10] Random walk in an alcove of an affine Weyl group, and non-colliding random walks on an interval
Grabiner, DJ
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2002, 97 (02) : 285 - 306

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