Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irregular sets and Central Limit Theorems for dependent triangular
  arrays   In previous papers, we studied the asymptotic behaviour of
$S_N(A,X)=(2N+1)^{-d/2}\sum_{n \in A_N} X_n,$ where $X$ is a centered,
stationary and weakly dependent random field, and $A_N=A \cap [-N,N]^d$, $A
\subset \mathbb{Z}^d$. This leads to the definition of asymptotically
measurable sets, which enjoy the property that $S_N(A;X)$ has a Gaussian weak
limit for any $X$ belonging to a certain class. Here we extend this type of
results to the case of weakly dependent triangular arrays and present an
application of this technique to regression models. Indeed, we prove that CLT
and related results hold for $X_n^N=\varphi(\xi_n^N,Y_n^N), n \in
\mathbb{Z}^d$, where $\varphi$ satisfies certain regularity conditions, $\xi$
and $Y$ are independent random fields, $\xi$ is weakly dependent and $Y$
satisfies some Strong Law of Large Numbers.

28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn