Quantitative homogenization of interacting particle systems
Quantitative homogenization of interacting particle systems
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DOI：
10.1214/22-aop1573
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
A. Giunti;Chenlin Gu;J. Mourrat
中科院分区：
文献类型：
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作者：
A. Giunti;Chenlin Gu;J. Mourrat
对于一类连续空间中的相互作用粒子系统，我们证明了体扩散矩阵的有限体积近似以代数速度收敛。我们考虑的模型是可逆的关于泊松测度的常密度，和非梯度型。我们的方法的灵感来自于最近的进展，在定量均匀化的椭圆方程。沿着的方式，我们开发适当的修改的Caccioppoli和多尺度Poincare不等式，这是独立的利益。
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 Poincare inequalities, which are of independent interest.