Related papers: Oscillations for order statistics of some discrete…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…
In this paper we study the asymptotic behavior of the maximum magnitude of a complex random polynomial with i.i.d. uniformly distributed random roots on the unit circle. More specifically, let $\{n_k\}_{k=1}^{\infty}$ be an infinite…
Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution function. The probability that these order statistics fall in disjoint, ordered…
Let $X_1,...,X_n$ be iid random vectors and $f\ge 0$ be a non-negative function. Let also $k(n) = {\rm Argmax}_{i=1,...,n} f(X_i)$. We are interested in the distribution of $X_{k(n)}$ and their limit theorems. In other words, what is the…
We consider a branching random walk in time-inhomogeneous random environment, in which all particles at generation $k$ branch into the same random number of particles $\mathcal{L}_{k+1}\ge 2$, where the $\mathcal{L}_k$, $k\in\mathbb{N}$,…
We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…
We determine the probability distribution for relative projective objects in an exceptional sequence of type $A_n$ of any length. We show that these events (the $j$-th object in an exceptional sequence of length $k\le n$ being relatively…
In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Consider a population of $N$ individuals, each having $d\geq 1$ different traits, and an additive measure, called dispersion, which rewards large pairwise separations between traits. The goal is to select $M\leq N$ individuals such that…
We present a comprehensive insight into counting distributions from the perspective of the combinants extracted from them. In particular, we focus on cases where these combinants exhibit oscillatory behavior that can provide an invaluable…
We determine upper and lower bounds for the number of maximum matchings (i.e., matchings of maximum cardinality) $m(T)$ of a tree $T$ of given order. While the trees that attain the lower bound are easily characterised, the trees with…
We show that the sequence of integers which have nearly the typical number of distinct prime factors forms a Poisson process. More precisely, for $\de$ arbitrarily small and positive, the nearest neighbor spacings between integers $n$ with…
The aim of this paper is to investigate the dynamics of a higher order system of rational difference equations. Our concentration is on boundedness character, the oscillatory, the existence of unbounded solutions and the global behavior of…
Multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We discuss the possible sources of these oscillations and their impact on our…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
Let i.i.d. symmetric Bernoulli random variables be associated to the edges of a binary tree having n levels. To any leaf of the tree, we associate the sum of variables along the path connecting the leaf with the tree root. Let M_n denote…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…