arXiv math/00040832000-04-12math.COmath.PRmath.RA

Loop-erased walks and total positivity

Sergey Fomin

备注：: 20 pages; 7 figures

英文摘要：

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.

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