VICIOUS WALKERS, FLOWS AND DIRECTED PERCOLATION

被引：22

作者：

ARROWSMITH, DK ^{[1
]}

MASON, P ^{[1
]}

ESSAM, JW ^{[1
]}

机构：

[1] UNIV LONDON,ROYAL HOLLOWAY & BEDFORD NEW COLL,DEPT MATH,EGHAM TW20 0EX,SURREY,ENGLAND

来源：

PHYSICA A | 1991年 / 177卷 / 1-3期

关键词：

D O I：

10.1016/0378-4371(91)90163-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is shown that the problem of m vicious random walkers is equivalent to the enumeration of integer natural flows on a directed square lattice with maximum flow m. An explicit formula for the number of such flows is given as a polynomial in m and is shown to have the same asymptotic form as Fisher's determinantal result. The expected number of such flows on directed bond or site percolation clusters is also a polynomial in m which reduces to the pair connectedness when m = 0. Consequently directed percolation may be seen as a problem of interacting vicious random walkers. Exact results for m = 1 and 2 are given.

引用

页码：267 / 272

页数：6