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Electrical Resistance of the Low Dimensional Critical Branching Random Walk

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Abstract

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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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK

    Antal A. Járai

  2. Department of Mathematics, University of British Columbia, 121-1984 Mathematics Rd, Vancouver, BC, V6T 1Z2, Canada

    Asaf Nachmias

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  1. Antal A. Járai
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  2. Asaf Nachmias
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Correspondence to Asaf Nachmias.

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Communicated by F. Toninelli

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Járai, A.A., Nachmias, A. Electrical Resistance of the Low Dimensional Critical Branching Random Walk. Commun. Math. Phys. 331, 67–109 (2014). https://doi.org/10.1007/s00220-014-2085-y

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  • DOI: https://doi.org/10.1007/s00220-014-2085-y

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