38 citations · 121 across the 24 of their papers we have counts for
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math.AP2018★ 23 cited
On mean field limit for Brownian particles with Coulomb interaction in 3D
Lei Li, Jian-Guo Liu, Pu Yu
In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit…
math.NA2018★ 2 cited
Large time behaviors of upwind schemes by jump processes
Lei Li, Jian-Guo Liu
We revisit the traditional upwind schemes for linear conservation laws in the viewpoint of jump processes, allowing studying upwind schemes using probabilistic tools. In particular…
math.PR2018★ 3 cited
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
Yuanyuan Feng, Lei Li, Jian-Guo Liu
We study the Markov semigroups for two important algorithms from machine learning: stochastic gradient descent (SGD) and online principal component analysis (PCA). We investigate t…