Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence in distribution of some particular self-interacting
  diffusions: the simulated annealing method   The present paper is concerned with some self-interacting diffusions
$(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to
stochastic differential equations: $$\mathrm{d}X_t = \mathrm{d}B_t - g(t)\nabla
V(X_t - \bar{\mu}_t) \mathrm{d}t$$ where $\bar{\mu}_t$ is the empirical mean of
the process $X$, $V$ is an asymptotically strictly convex potential and $g$ is
a given function. The authors have still studied the ergodic behavior of $X$
and proved that it is strongly related to $g$. We go further and give necessary
and sufficient conditions (for small $g$'s) in order that $X$ converges in
probability to $X_\infty$ (which is related to the global minima of $V$).

24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th