SCALING LIMIT FOR A LONG-RANGE DIVISIBLE SANDPILE

被引：4

作者：

Frometa, Susana ^{[1
,2
]}

Jara, Milton ^{[1
]}

机构：

[1] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil

[2] Univ Fed Rio Grande do Sul, Rua Bento Goncalves 9500, BR-91509900 Porto Alegre, RS, Brazil

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 03期

关键词：

divisible sandpile; Green's functions; alpha-stable laws; fractional Laplacian; obstacle problem; OBSTACLE PROBLEM; AGGREGATION;

D O I：

10.1137/16M1068062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the scaling limit of a divisible sandpile model associated with a truncated alpha-stable random walk. We prove that the limiting distribution is related to an obstacle problem for a truncated fractional Laplacian. We also provide, as a fundamental tool, precise asymptotic expansions for the corresponding rescaled discrete Green's functions. In particular, the convergence rate of these Green's functions to its continuous counterpart is derived.

引用

页码：2317 / 2361

页数：45

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