Electrical Resistance of the Low Dimensional Critical Branching Random Walk

Communications in Mathematical Physics(2014)

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摘要
We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O ( n 1- α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385–431, 2008 ).
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关键词
Random Walk,Triangle Inequality,Side Branch,Vertex Versus,Effective Resistance
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