论文标题
Monge-ampère重力作为$γ$ - 效率良好的限制
Monge-Ampère gravitation as a $Γ$-limit of good rate functions
论文作者
论文摘要
Monge-ampère重力是对古典牛顿引力的修改，其中线性泊松方程被非线性的monge-ampère方程所取代。本文与第三作者的先前作品精神的精神[Monge-ampère引力的双重偏差原理，2016年的双重偏差原则，2016年，对Monge-Ampère的重力的严格推导，用于有限数量的粒子。此推导的主要步骤是$γ-$融合的良好利率函数对应于一个大偏差原理的单参数家族。令人惊讶的是，派生的模型包括耗散现象。作为例证，我们证明它会导致一个空间维度的粘性碰撞。
Monge-Ampère gravitation is a modification of the classical Newtonian gravitation where the linear Poisson equation is replaced by the nonlinear Monge-Ampère equation. This paper is concerned with the rigorous derivation of Monge-Ampère gravitation for a finite number of particles from the stochastic model of a Brownian point cloud, in the spirit of a previous work by the third author [A double large deviation principle for Monge-Ampère gravitation, 2016]. The main step in this derivation is the $Γ-$convergence of the good rate functions corresponding to a one-parameter family of large deviation principles. Surprisingly, the derived model includes dissipative phenomena. As an illustration, we show that it leads to sticky collisions in one space dimension.
