Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for the concentration functions in the Littlewood--Offord
  problem   Let $X,X_1,...,X_n$ be independent identically distributed random variables.
In this paper we study the behavior of the concentration functions of the
weighted sums $\sum\limits_{k=1}^{n}a_k X_k$ with respect to the arithmetic
structure of coefficients $a_k$. Such concentration results recently became
important in connection with investigations about singular values of random
matrices. In this paper we formulate and prove some refinements of a result of
Vershynin (R. Vershynin, Invertibility of symmetric random matrices,
arXiv:1102.0300. (2011). Published in Random Structures and Algorithms, v. 44,
no. 2, 135--182 (2014)).

32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph