Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invariance principle for stochastic heat equations with periodic
  coefficients   We investigate the asymptotic behaviors of the solution $u(t, \cdot)$ to a
stochastic heat equation with a periodic, gradient-type nonlinear term. We
extend the central limit theorem for finite-dimensional diffusions to
infinite-dimensional settings. Due to our results, $\frac{1}{\sqrt t}u(t,
\cdot)$ converges weakly to a centered Gaussian variable whose covariance
operator is described through Poisson equations. Different from the
finite-dimensional case, the fluctuation in space vanishes in the limit
distribution. Furthermore, we verify the tightness and present an invariance
principle for $\{\epsilon u(\epsilon^{-2}t, \cdot)\}_{t \in [0, T]}$ as
$\epsilon \downarrow 0$.

29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys