Logarithmic correction to resistance

Antal A. Jarai; Dante Mata Lopez

doi:10.1214/21-AIHP1213

Logarithmic correction to resistance

Antal A. Jarai, Dante Mata Lopez

Centro de Investigación en Matemáticas

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

1 Citation (SciVal)

Abstract

We study the trace of the incipient infinite oriented branching random walk in Zd×Z+ when the dimension is d=6. Under suitable moment assumptions, we show that the electrical resistance between the root and level n is O(nlog^-ξn) for a ξ>0 that does not depend on details of the model.

Original language	English
Pages (from-to)	1775-1807
Number of pages	33
Journal	Annales de l'Institut Henri Poincaré: Probabilités et Statistiques
Volume	58
Issue number	3
Early online date	14 Jul 2022
DOIs	https://doi.org/10.1214/21-AIHP1213
Publication status	Published - 31 Aug 2022

Bibliographical note

Funding Information:
The second author was supported by CONACyT Mexico Grant 836354.

Keywords

Anomalous diffusion
Branching random walk
Electrical resistance

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/21-AIHP1213

https://arxiv.org/abs/2006.03988Licence: CC BY

Cite this

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title = "Logarithmic correction to resistance",

abstract = "We study the trace of the incipient infinite oriented branching random walk in Zd×Z+ when the dimension is d=6. Under suitable moment assumptions, we show that the electrical resistance between the root and level n is O(nlog-ξn) for a ξ>0 that does not depend on details of the model.",

keywords = "Anomalous diffusion, Branching random walk, Electrical resistance",

author = "Jarai, {Antal A.} and {Mata Lopez}, Dante",

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AB - We study the trace of the incipient infinite oriented branching random walk in Zd×Z+ when the dimension is d=6. Under suitable moment assumptions, we show that the electrical resistance between the root and level n is O(nlog-ξn) for a ξ>0 that does not depend on details of the model.

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KW - Branching random walk

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Logarithmic correction to resistance

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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