Electrical Resistance of the Low Dimensional Critical Branching Random Walk

Antal A. Járai; Asaf Nachmias

doi:10.1007/s00220-014-2085-y

Electrical Resistance of the Low Dimensional Critical Branching Random Walk

Antal A. Járai, Asaf Nachmias^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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).

Original language	English
Pages (from-to)	67-109
Number of pages	43
Journal	Communications in Mathematical Physics
Volume	331
Issue number	1
DOIs	https://doi.org/10.1007/s00220-014-2085-y
State	Published - Aug 2014
Externally published	Yes

Funding

Funders	Funder number
National Science Foundation
Natural Sciences and Engineering Research Council of Canada

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10.1007/s00220-014-2085-y

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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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AB - 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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Electrical Resistance of the Low Dimensional Critical Branching Random Walk

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