图上Fokker-Planck方程的熵耗散
Entropy dissipation of Fokker-Planck equations on graphs
摘要：
本文研究图上的非线性Fokker-Planck方程，它是关于离散Wasserstein度量的支撑在节点上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。我们表明，该解决方案收敛到吉布斯措施指数速度快，可以给出解析。这个渐近速率的连续模拟与Yano公式有关。
英文摘要：
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 with a rate that can be given analytically. The continuous analog of this asymptotic rate is related to the Yano's formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
