Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of the thermodynamic limit for random-field random surfaces   We study random surfaces with a uniformly convex gradient interaction in the
presence of quenched disorder taking the form of a random independent external
field. Previous work on the model has focused on proving existence and
uniqueness of infinite-volume gradient Gibbs measures with a given tilt and on
studying the fluctuations of the surface and its discrete gradient.
  In this work we focus on the convergence of the thermodynamic limit,
establishing convergence of the finite-volume distributions with Dirichlet
boundary conditions to translation-covariant (gradient) Gibbs measures.
Specifically, it is shown that, when the law of the random field has finite
second moment and is symmetric, the distribution of the gradient of the surface
converges in dimensions $d\geq4$ while the distribution of the surface itself
converges in dimensions $d\geq 5$. Moreover, a power-law upper bound on the
rate of convergence in Wasserstein distance is obtained. The results partially
answer a question discussed by Cotar and K\"ulske

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph