Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequalities and tail bounds for elementary symmetric polynomial with
  applications   We study the extent of independence needed to approximate the product of
bounded random variables in expectation, a natural question that has
applications in pseudorandomness and min-wise independent hashing.
  For random variables whose absolute value is bounded by $1$, we give an error
bound of the form $\sigma^{\Omega(k)}$ where $k$ is the amount of independence
and $\sigma^2$ is the total variance of the sum. Previously known bounds only
applied in more restricted settings, and were quanitively weaker. We use this
to give a simpler and more modular analysis of a construction of min-wise
independent hash functions and pseudorandom generators for combinatorial
rectangles due to Gopalan et al., which also slightly improves their
seed-length.
  Our proof relies on a new analytic inequality for the elementary symmetric
polynomials $S_k(x)$ for $x \in \mathbb{R}^n$ which we believe to be of
independent interest. We show that if $|S_k(x)|,|S_{k+1}(x)|$ are small
relative to $|S_{k-1}(x)|$ for some $k>0$ then $|S_\ell(x)|$ is also small for
all $\ell > k$. From these, we derive tail bounds for the elementary symmetric
polynomials when the inputs are only $k$-wise independent.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys