Loop-erased walks and total positivity
组合数学
2007-05-23 v1 概率论
环与代数
摘要
We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative coefficients. A combinatorial explanation of this phenomenon involves loop-erased walks. Applications include total positivity of hitting matrices of Brownian motion in planar domains.
引用
@article{arxiv.math/0004083,
title = {Loop-erased walks and total positivity},
author = {Sergey Fomin},
journal= {arXiv preprint arXiv:math/0004083},
year = {2007}
}
备注
20 pages; 7 figures