Stabilization of dla in a wedge

Eviatar B. Procaccia; Ron Rosenthal; Yuan Zhang

doi:10.1214/20-EJP446

Stabilization of dla in a wedge

Eviatar B. Procaccia, Ron Rosenthal, Yuan Zhang

Mathematics

Technion - Israel Institute of Technology

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

Abstract

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than µ/4, there is some a > 2 such that almost surely, for all R^a large enough, after time Ra all new particles attached to the DLA will be at distance larger than R from the origin. Furthermore, we provide estimates on the size of R under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.

Original language	English
Article number	42
Journal	Electronic Journal of Probability
Volume	25
DOIs	https://doi.org/10.1214/20-EJP446
State	Published - 2020

Keywords

Beurling estimate
Diffusion limited aggregation
Growth model
Harmonic measure
Reflected random walk
Stabilization

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/20-EJP446

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abstract = "We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than µ/4, there is some a > 2 such that almost surely, for all Ra large enough, after time Ra all new particles attached to the DLA will be at distance larger than R from the origin. Furthermore, we provide estimates on the size of R under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.",

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author = "Procaccia, {Eviatar B.} and Ron Rosenthal and Yuan Zhang",

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T1 - Stabilization of dla in a wedge

AU - Procaccia, Eviatar B.

AU - Rosenthal, Ron

AU - Zhang, Yuan

PY - 2020

Y1 - 2020

N2 - We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than µ/4, there is some a > 2 such that almost surely, for all Ra large enough, after time Ra all new particles attached to the DLA will be at distance larger than R from the origin. Furthermore, we provide estimates on the size of R under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.

AB - We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than µ/4, there is some a > 2 such that almost surely, for all Ra large enough, after time Ra all new particles attached to the DLA will be at distance larger than R from the origin. Furthermore, we provide estimates on the size of R under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.

KW - Beurling estimate

KW - Diffusion limited aggregation

KW - Growth model

KW - Harmonic measure

KW - Reflected random walk

KW - Stabilization

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U2 - 10.1214/20-EJP446

DO - 10.1214/20-EJP446

M3 - مقالة

SN - 1083-6489

VL - 25

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 42

ER -

Stabilization of dla in a wedge

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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