论文标题
平均场雪崩和分支扩散的等效性：从Brownian Force模型到超棕色运动
Equivalence of mean-field avalanches and branching diffusions: From the Brownian force model to the super-Brownian motion
论文作者
论文摘要
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 {\it space-embedded} Galton-Watson trees.特别是，最近在平均场雪崩中发现的确切可溶性（重新）（重新）（“ instanton方程”）映射到所谓的Dawson-Watanabe 1968二元性属性上。鉴于这种对应关系，我们比较了在两个字段中独立获得的结果，并将其中的一些从一个磁场传输到另一个字段。特别是，我们讨论了布朗尼分支运动的缩放限制，该运动映射到平均场雪崩的连续性场理论上
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 {\it 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
