Stationary DLA is Well Defined

Eviatar B. Procaccia; Jiayan Ye; Yuan Zhang

doi:10.1007/s10955-020-02619-8

Stationary DLA is Well Defined

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

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

6 Scopus citations

Abstract

In this paper, we construct an infinite stationary diffusion limited aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. This model was suggested by Itai Benjamini. The main issue is a known problem in DLA models, the long range effects of large arms. In this paper we overcome this difficulty via a multi-scale argument controlling the dynamical discrepancies created on all scales while running two coupled SDLA on different starting configurations.

Original language	English
Pages (from-to)	1089-1111
Number of pages	23
Journal	Journal of Statistical Physics
Volume	181
Issue number	4
DOIs	https://doi.org/10.1007/s10955-020-02619-8
State	Published - 1 Nov 2020
Externally published	Yes

Keywords

Diffusion limited aggregation
Interacting particle system
Stationary harmonic measure

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-020-02619-8

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abstract = "In this paper, we construct an infinite stationary diffusion limited aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. This model was suggested by Itai Benjamini. The main issue is a known problem in DLA models, the long range effects of large arms. In this paper we overcome this difficulty via a multi-scale argument controlling the dynamical discrepancies created on all scales while running two coupled SDLA on different starting configurations.",

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KW - Stationary harmonic measure

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Stationary DLA is Well Defined

Abstract

Keywords

ASJC Scopus subject areas

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