论文标题
相互作用粒子系统的定量均质化
Quantitative homogenization of interacting particle systems
论文作者
论文摘要
对于连续空间中的一类相互作用的粒子系统，我们表明散装扩散矩阵的有限体积近似值以代数速率收敛。我们认为的模型相对于恒定密度的泊松度量是可逆的，并且是非梯度类型的。我们的方法是受椭圆方程定量均质化的最新进展的启发。在此过程中，我们开发了具有独立利益的Caccioppoli和多尺度庞加尔不平等现象的适当修改。
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of non-gradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincaré inequalities, which are of independent interest.
