SCALING LIMIT OF DLA ON A LONG LINE SEGMENT

Yingxin Mu; Eviatar B. Procaccia; Yuan Zhang

doi:10.1090/tran/8771

SCALING LIMIT OF DLA ON A LONG LINE SEGMENT

Yingxin Mu, Eviatar B. Procaccia, Yuan Zhang

Data and Decision Sciences

Technion - Israel Institute of Technology

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

Abstract

In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.

Original language	English
Pages (from-to)	8769-8806
Number of pages	38
Journal	Transactions of the American Mathematical Society
Volume	375
Issue number	12
DOIs	https://doi.org/10.1090/tran/8771
State	Published - Dec 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/8771

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title = "SCALING LIMIT OF DLA ON A LONG LINE SEGMENT",

abstract = "In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.",

author = "Yingxin Mu and Procaccia, {Eviatar B.} and Yuan Zhang",

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year = "2022",

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doi = "10.1090/tran/8771",

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N2 - In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.

AB - In this paper, we prove that the bulk of 2-dimensional DLA starting from a long line segment on the x-axis has a scaling limit to the stationary DLA. The main phenomenological difficulty is the multi-scale, non-monotone interaction of the DLA arms. We overcome this via a coupling scheme between the two processes and an intermediate DLA process with absorbing mesoscopic boundary segments. Our result allows to import results from the more amenable infinite stationary DLA process to the more physical finite aggregations.

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M3 - مقالة

SN - 0002-9947

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 12

ER -

SCALING LIMIT OF DLA ON A LONG LINE SEGMENT

Abstract

All Science Journal Classification (ASJC) codes

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