相关论文: Generalized Hanson-Wright Inequality for Random Te…

This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order $p \ge 3:$ when the effective ranks of the covariances of the component…

Consider $N\times N$ symmetric one-dimensional random band matrices with general distribution of the entries and band width $W \geq N^{3/4+\varepsilon}$ for any $\varepsilon>0$. In the bulk of the spectrum and in the large $N$ limit, we…

The generalized Kneser graph $K(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is the graph whose vertices are the $k$-subsets of $\{1,\dots,n\}$ with two vertices adjacent if and only if they share less than $t$ elements. We determine the…

In this work we present concentration inequalities for the sum $S_n$ of independent integer-valued not necessary indentically distributed random variables, where each variable has tail function that can be bounded by some power function…

Starting from the free field realization of Kac-Moody Lie algebra, we define a generalized Yang-Yang function. Then for the Lie algebra of type $A_{n}$, we derive braiding and fusion matrix by braiding the thimble from the generalized…

In this paper, we provide three applications for $f$-divergences: (i) we introduce Sanov's upper bound on the tail probability of the sum of independent random variables based on super-modular $f$-divergence and show that our generalized…

We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…

This work is devoted to explore fundamental aspects of the spectral properties of few-body general operators. We first consider the following question: when we know the probability distributions of a set of observables, what can we way on…

We study the central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with $d$. Our main…

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…

We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…

Both complete decoupling and tangent decoupling are classical tools aiming to compare two random processes where one has a weaker dependence structure. We give a new proof for the complete decoupling inequality, which provides a lower bound…

This article addresses an equidistribution problem concerning the zeros of systems of random holomorphic sections of positive line bundles on compact K\"{a}hler manifolds and random polynomials on $\mathbb{C}^{m}$ in the setting of the…

The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The…

We consider the problem of discriminating between two different states of a finite quantum system in the setting of large numbers of copies, and find a closed form expression for the asymptotic exponential rate at which the specified error…

We derive a resummation formula for a $k_T$-dependent parton distribution function at threshold, where $k_T$ is a parton transverse momentum. The derivation requires infrared cutoffs for both longitudinal and transverse loop momenta as…

A difficult problem in the theory of random tensors is to calculate the expectation values of polynomials in the tensor entries, even in the large N limit and in a Gaussian distribution. Here we address this issue, focusing on a family of…

In this paper, we quantify the rate of convergence between the distribution of number of zeros of random trigonometric polynomials (RTP) with i.i.d. centered random coefficients and the number of zeros of a stationary centered Gaussian…

Using Wilson's Haar basis in $\R^n$, which is different than the usual tensor product Haar functions, we define its associated dyadic paraproduct in $\R^n$. We can then extend "trivially" Beznosova's Bellman function proof of the linear…

In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…