Gamma Calculus Beyond Villani and Explicit Convergence Estimates for Langevin Dynamics with Singular Potentials
Gamma Calculus Beyond Villani and Explicit Convergence Estimates for Langevin Dynamics with Singular Potentials
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DOI：
10.1007/s00205-021-01664-1
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发表时间：
2021-06-08
影响因子：
2.5
通讯作者：
Herzog, David P.
中科院分区：
文献类型：
--
作者：
Baudoin, Fabrice;Gordina, Maria;Herzog, David P.
我们应用伽玛演算的亚椭圆和非对称设置的朗之万动力学在一般条件下的潜力。这种扩展使我们能够提供明确的估计的收敛速度（这是指数）平衡的动态加权H-1（μ）的意义上，μ表示系统的唯一不变的概率测度。一般结果适用于奇异势，如著名的Lennard-Jones相互作用和限制井，它适用于在这种情况下，估计收敛速度时，系统中的粒子数N是大的。
We apply Gamma calculus to the hypoelliptic and non-symmetric setting of Langevin dynamics under general conditions on the potential. This extension allows us to provide explicit estimates on the convergence rate (which is exponential) to equilibrium for the dynamics in a weighted H-1(mu) sense, mu denoting the unique invariant probability measure of the system. The general result holds for singular potentials, such as the well-known Lennard-Jones interaction and confining well, and it is applied in such a case to estimate the rate of convergence when the number of particles N in the system is large.