A Convergence Rate for Extended-Source Internal DLA in the Plane

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-10-16 DOI:10.1007/s11118-023-10102-8

David Darrow

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引用次数: 2

Abstract

Abstract Internal DLA (IDLA) is an internal aggregation model in which particles perform random walks from the origin, in turn, and stop upon reaching an unoccupied site. Levine and Peres showed that, when particles start instead from fixed multiple-point distributions, the modified IDLA processes have deterministic scaling limits related to a certain obstacle problem. In this paper, we investigate the convergence rate of this “extended source” IDLA in the plane to its scaling limit. We show that, if $$\delta $$ δ is the lattice size, fluctuations of the IDLA occupied set are at most of order $$\delta ^{3/5}$$ δ 3 / 5 from its scaling limit, with probability at least $$1-e^{-1/\delta ^{2/5}}$$ 1 - e - 1 / δ 2 / 5 .

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平面内扩展源DLA的收敛速率研究

内部DLA (IDLA)是一种内部聚集模型，其中粒子依次从原点随机行走，并在到达一个未被占用的位置时停止。Levine和Peres表明，当粒子从固定的多点分布开始时，改进的IDLA过程具有与特定障碍问题相关的确定性缩放限制。在本文中，我们研究了这种“扩展源”IDLA在平面上的收敛速度到它的缩放极限。我们证明，当$$\delta $$ δ为晶格尺寸时，IDLA占位集的波动距离其标度极限最多为$$\delta ^{3/5}$$ δ 3 / 5阶，且概率至少为$$1-e^{-1/\delta ^{2/5}}$$ 1 - e - 1 / δ 2 / 5。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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