ENTROPY DISSIPATION OF FOKKER-PLANCK EQUATIONS ON GRAPHS
ENTROPY DISSIPATION OF FOKKER-PLANCK EQUATIONS ON GRAPHS
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DOI：
10.3934/dcds.2018215
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发表时间：
2018-10-01
影响因子：
1.1
通讯作者：
Zhou, Haomin
中科院分区：
文献类型：
--
作者：
Chow, Shui-Nee;Li, Wuchen;Zhou, Haomin
我们研究图上的非线性 Fokker-Planck 方程，它是节点上支持的关于离散 Wasserstein 度量的概率测度空间中的梯度流。驱动梯度流的能量泛函由玻尔兹曼熵、线性势和二次相互作用能组成。我们证明该解以指数速度快速收敛到吉布斯测度。这种渐近率的连续模拟与矢野公式有关。
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the space of probability measures supported on the nodes with respect to the discrete Wasserstein metric. The energy functional driving the gradient flow consists of a Boltzmann entropy, a linear potential and a quadratic interaction energy. We show that the solution converges to the Gibbs measures exponentially fast. The continuous analog of this asymptotic rate is related to the Yano's formula.