One-dimensional long-range diffusion limited aggregation II: The transient case

Gideon Amir; Omer Angel; Gady Kozma

doi:10.1214/16-AAP1248

One-dimensional long-range diffusion limited aggregation II: The transient case

Gideon Amir, Omer Angel, Gady Kozma

Bar-Ilan University, Weizmann Institute of Science

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

Abstract

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps.We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.

Original language	English
Pages (from-to)	1886-1922
Number of pages	37
Journal	Annals of Applied Probability
Volume	27
Issue number	3
DOIs	https://doi.org/10.1214/16-AAP1248
State	Published - Jun 2017

Keywords

Diffusion limited aggregation
Growth process
Harmonic measure
Transient random walk

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/16-AAP1248

Cite this

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title = "One-dimensional long-range diffusion limited aggregation II: The transient case",

abstract = "We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps.We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.",

keywords = "Diffusion limited aggregation, Growth process, Harmonic measure, Transient random walk",

author = "Gideon Amir and Omer Angel and Gady Kozma",

note = "Publisher Copyright: {\textcopyright} 2017 Institute of Mathematical Statistics.",

year = "2017",

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doi = "10.1214/16-AAP1248",

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T2 - The transient case

AU - Amir, Gideon

AU - Angel, Omer

AU - Kozma, Gady

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N2 - We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps.We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.

AB - We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps.We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this paper, we handle the case of transient walks.

KW - Diffusion limited aggregation

KW - Growth process

KW - Harmonic measure

KW - Transient random walk

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DO - 10.1214/16-AAP1248

M3 - مقالة

SN - 1050-5164

VL - 27

SP - 1886

EP - 1922

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 3

ER -

One-dimensional long-range diffusion limited aggregation II: The transient case

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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