  We study an interacting particle system in $\mathbf{R}^d$ motivated by Stein
variational gradient descent [Q. Liu and D. Wang, NIPS 2016], a deterministic
algorithm for sampling from a given probability density with unknown
normalization. We prove that in the large particle limit the empirical measure
of the particle system converges to a solution of a non-local and nonlinear
PDE. We also prove global existence, uniqueness and regularity of the solution
to the limiting PDE. Finally, we prove that the solution to the PDE converges
to the unique invariant solution in long time limit.

Analysis of PDEs;Methodology;Machine Learning