相关论文: Explicit Universal Bounds for Cumulants via Moment…

Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…

We present multivariate unbiased estimators for second, third, and fourth order cumulants $C_2(x,y)$, $C_3(x,y,z)$, and $C_4(x,y,z,w)$. Many relevant new estimators are derived for cases where some variables are average-free or pairs of…

We establish sufficient conditions for the existence, and derive explicit formulas for the $\kappa$'th moments, $\kappa \geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In…

In this paper we construct cumulants for stable random matrix models with single trace interactions of arbitrarily high even order. We obtain explicit and convergent expansions for it and we prove that it is an analytic function inside a…

In this paper we show that if large jumps of an It\^o-semimartingale $X$ have a finite $p$-moment, $p>0$, the radial part of its drift is dominated by $-|X|^\kappa$ for some $\kappa\geq -1$, and the balance condition $p+\kappa>1$ holds…

Let $C\subseteq \{1,\ldots,k\}^n$ be such that for any $k$ distinct elements of $C$ there exists a coordinate where they all differ simultaneously. Fredman and Koml\'os studied upper and lower bounds on the largest cardinality of such a set…

We investigate the extent to which the phenomenon of Brownian entropic repulsion is universal. Consider a Brownian motion conditioned on the event $\mathcal{E}$ -- that its local time is bounded everywhere by 1. This event has probability…

This paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a…

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants…

We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the…

When existing, cumulants can provide valuable information about a given distribution and can in principle be used to either fully reconstruct or approximate the parent distribution function. A previously reported cumulant expansion approach…

We compute the exact asymptotics for the cumulants of linear statistics associated with the zeros counting measure of a large class of real Gaussian processes. Precisely, we show that if the underlying covariance function is regular and…

We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals admitting a uniform integrable tail-quantile envelope. The…

We establish conditions for uniform $r$-th moment bound of certain $\R^d$-valued functions of a discrete-time stochastic process taking values in a general metric space. The conditions include an appropriate negative drift together with a…

This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…

To find moments of various estimators related to Autoregressive models of Statistics, one first needs the cumulants of products of two Normally distributed random variables. The purpose of this article is to derive the corresponding…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

The spectral properties of positive maps are pivotal for understanding the dynamics of quantum systems interacting with their environment. Furthermore, central problems in quantum information such as the characterization of entanglement can…

In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure…

In this paper, we introduce a novel approach for bounding the cumulant generating function (CGF) of a Dirichlet process (DP) $X \sim \text{DP}(\alpha \nu_0)$, using superadditivity. In particular, our key technical contribution is the…