论文标题
在边界驱动的排除中，超扩散行为扩散
Diffusive to super-diffusive behavior in boundary driven exclusion
论文作者
论文摘要
本文的目的是研究跳远的对称排除过程的流体动力限制，并与特定关键方向的无限扩展的储层接触。跳跃是根据可以具有有限或无限方差的过渡概率给出的，而流体动力方程在后一种情况下是一个扩散方程，在后一种情况下是分数方程。在这项工作中，我们处理关键案例，即，当方差是无限的，并且随系统的大小而对数增长。从扩散到超扩散行为的过渡就是这种情况。
The purpose of this article is to study the hydrodynamic limit of the symmetric exclusion process with long jumps and in contact with infinitely extended reservoirs for a particular critical regime. The jumps are given in terms of a transition probability that can have finite or infinite variance and the hydrodynamic equation is a diffusive equation, in the former case, or a fractional equation, in the latter case. In this work we treat the critical case, that is, when the variance is infinite and grows logarithmically with the size of the system. This is the case in which there is a transition from diffusive to super-diffusive behavior.
