Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequalities for sums of random variables in noncommutative probability
  spaces   In this paper, we establish an extension of a noncommutative Bennett
inequality with a parameter $1\leq r\leq2$ and use it together with some
noncommutative techniques to establish a Rosenthal inequality. We also present
a noncommutative Hoeffding inequality as follows: Let $(\mathfrak{M}, \tau)$ be
a noncommutative probability space, $\mathfrak{N}$ be a von Neumann subalgebra
of $\mathfrak{M}$ with the corresponding conditional expectation
$\mathcal{E}_{\mathfrak{N}}$ and let subalgebras
$\mathfrak{N}\subseteq\mathfrak{A}_j\subseteq\mathfrak{M}\,\,(j=1, \cdots, n)$
be successively independent over $\mathfrak{N}$. Let $x_j\in\mathfrak{A}_j$ be
self-adjoint such that $a_j\leq x_j\leq b_j$ for some real numbers $a_j<b_j$
and $\mathcal{E}_{\mathfrak{N}}(x_j)=\mu$ for some $\mu\geq 0$ and all $1\leq
j\leq n$. Then for any $t>o$ it holds that \begin{eqnarray*} {\rm
Prob}\left(\left|\sum_{j=1}^n x_j-n\mu\right|\geq t\right)\leq 2
\exp\left\{\frac{-2t^2}{\sum_{j=1}^n(b_j-a_j)^2}\right\}. \end{eqnarray*}

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin