Related papers: Random gap processes and asymptotically complete s…
The goal of this paper is to analyse the asymptotic behavior of the cycle process and the total number of cycles of weighted and generalized weighted random permutations which are relevant models in physics and which extend the Ewens…
Motivated by applications in bioinformatics, we consider the word collector problem, i.e. the expected number of calls to a random weighted generator of words of length $n$ before the full collection is obtained. The originality of this…
We investigate the asymptotic structure of a random perfect graph $P_n$ sampled uniformly from the perfect graphs on vertex set $\{1,\ldots,n\}$. Our approach is based on the result of Pr\"omel and Steger that almost all perfect graphs are…
The purpose of this note is to study asymptotic zero distribution of multivariate random polynomials as their degrees grow. For a smooth weight function with super logarithmic growth at infinity, we consider random linear combinations of…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be…
A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for…
The class of generating functions for completely monotone sequences (moments of finite positive measures on $[0,1]$) has an elegant characterization as the class of Pick functions analytic and positive on $(-\infty,1)$. We establish this…
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…
We treat a random number generation from an i.i.d. probability distribution of $P$ to that of $Q$. When $Q$ or $P$ is a uniform distribution, the problems have been well-known as the uniform random number generation and the resolvability…
In this paper, we are interested in the asymptotic behaviour of the sequence of processes $(W_n(s,t))_{s,t\in[0,1]}$ with \begin{equation*} W_n(s,t):=\sum_{k=1}^{\lfloor nt\rfloor}\big(1_{\{\xi_{S_k}\leq s\}}-s\big) \end{equation*} where…
We give an exact formula for the value of the derivative at zero of the gap probability in finite n x n Gaussian ensembles. As n goes to infinity our computation provides an asymptotic (with an explicit constant) of the order n^(1/2). As a…
In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…
In this paper, we consider fully connected feed-forward deep neural networks where weights and biases are independent and identically distributed according to Gaussian distributions. Extending previous results (Matthews et al., 2018a;b;…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
The complete convergence for weighted sums of sequences of independent, identically distributed random variables under sublinear expectations space was studied. By moment inequality and truncation methods, we establish the equivalent…
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even integer base-$s$ expansion with two redundant digits form a…
To each sequence $(a_n)$ of positive real numbers we associate a growing sequence $(T_n)$ of continuous trees built recursively by gluing at step $n$ a segment of length $a_n$ on a uniform point of the pre-existing tree, starting from a…