Related papers: Exponential bounds for the hypergeometric distribu…

The geometric sum plays a significant role in risk theory and reliability theory \cite{Kala97} and a prototypical example of the geometric sum is R\'enyi's theorem~\cite{Renyi56} saying a sequence of suitably parameterised geometric sums…

The paper reexamines an argument by Talagrand that leads to a remarkable exponential tail bound for the concentration of probability near a set. The main novelty is the replacement of a mysterious Calculus inequality by an application of…

Let $p$ be a prime number, $X$ be an absolutely irreducible affine plane curve over $\mathbb{F}_p$, and $g,f\in\mathbb{F}_p(x,y)$. We study the distribution of the values of the hybrid exponential sums S_n on $n\in\mathcal{I}$ for some…

We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient…

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…

We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results…

We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set…

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

Let X_1,..., X_n be independent Bernoulli random variables and $f$ a function on {0,1}^n. In the well-known paper (Talagrand1994) Talagrand gave an upper bound for the variance of f in terms of the individual influences of the X_i's. This…

We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…

In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…

Generalization error bounds are essential for comprehending how well machine learning models work. In this work, we suggest a novel method, i.e., the Auxiliary Distribution Method, that leads to new upper bounds on expected generalization…

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…

We discuss some open problems concerning the maximal spread of coherent distributions. We prove a sharp bound on $\mathbb{E}|X-Y|^{\alpha}$ for $(X,Y)$ coherent and $\alpha \le 2$, and establish a novel connection between coherent…

Let $X_1,\ldots,X_n$ be independent identically distributed random vectors in $\mathbb{R}^d$. We consider upper bounds on $\max_x \mathbb{P}(a_1X_1+\cdots+a_nX_n=x)$ under various restrictions on $X_i$ and the weights $a_i$. When…

In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a well-know inversion formula for Laplace…

We study in detail the class of even polynomials and their behavior with respect to finite free convolutions. To this end, we use some specific hypergeometric polynomials and a variation of the rectangular finite free convolution to…

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously…

Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of opportunity access as the object of…