Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small noise spectral gap asymptotics for a large system of nonlinear
  diffusions   We study the $L^2$ spectral gap of a large system of strongly coupled
diffusions on unbounded state space and subject to a double-well potential.
This system can be seen as a spatially discrete approximation of the stochastic
Allen-Cahn equation on the one-dimensional torus. We prove upper and lower
bounds for the leading term of the spectral gap in the small temperature regime
with uniform control in the system size. The upper bound is given by an
Eyring-Kramers-type formula. The lower bound is proven to hold also for the
logarithmic Sobolev constant. We establish a sufficient condition for the
asymptotic optimality of the upper bound and show that this condition is
fulfilled under suitable assumptions on the growth of the system size. Our
results can be reformulated in terms of a semiclassical Witten Laplacian in
large dimension.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph