期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 55, 期 39, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac8d3b
关键词
avalanches; branching processes; super Brownian motion; interface depinning; Galton Watson trees; non linear PDE
资金
- PSL [ANR-10-IDEX-0001-02-PSL]
- ANR [ANR-17-CE30-0027-01 RaMaTraF]
This study reveals the equivalence between the mean-field theory of avalanches in the dynamics of elastic interfaces (BFM) and the super-Brownian motion (SBM) in probability theory, along with some results that can be transferred between the two fields.
We point out that the mean-field theory of avalanches in the dynamics of elastic interfaces, the so-called Brownian force model (BFM) developed recently in non-equilibrium statistical physics, is equivalent to the so-called super-Brownian motion (SBM) developed in probability theory, a continuum limit of branching processes related to space-embedded Galton-Watson trees. In particular the exact solvability property recently (re-)discovered from the field theory in mean-field avalanches (the 'instanton equation') maps onto the so-called Dawson-Watanabe 1968 duality property. In the light of this correspondence we compare the results obtained independently in the two fields, and transport some of them from one field to the other. In particular, we discuss a scaling limit of the branching Brownian motion which maps onto the continuum field theory of mean-field avalanches.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据