Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-time behaviors of mean-field interacting particle systems related
  to McKean-Vlasov equations   In this paper, we investigate gradient estimate of the Poisson equation and
the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform
in the number of particles, and uniform-in-time propagation of chaos for the
mean-field weakly interacting particle system related to McKean-Vlasov
equation. By means of the known approximate componentwise reflection coupling
and with the help of some new cost function, we obtain explicit estimates for
those three problems, avoiding the technical conditions in the known results.
Our results apply when the confinement potential $V$ has many wells, the
interaction potential $W$ has bounded second mixed derivative $\nabla^2_{xy}W$
which should be not too big so that there is no phase transition. As an
application, we obtain the concentration inequality of the mean-field
interacting particle system with explicit and sharp constants, uniform in time.
Several examples are provided to illustrate the results.

17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th