Related papers: Normal approximation for isolated balls in an urn …

We analyze the asymptotic behavior of the average maximal number of balls in a bin obtained by throwing uniformly at random $r$ balls without replacement into $n$ bins, $T$ times. Writing the expected maximum as $\frac{r}{n}T+…

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 paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$,…

Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. Recently, Laruelle and Pag\`es (2013) presented a link between the stochastic approximation and response-adaptive…

We describe a universality class of the transitions of a generalized P\'{o}lya urn by studying the asymptotic behavior of the normalized correlation function $C(t)$ using finite-size scaling analysis. $X(1),X(2),\cdots$ are the successive…

Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw…

Let $\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\ell_p$-norm. For each $N\in\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\in\mathbb{N}$ and consider the volume of $\mathbb{B}_p^N$…

We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

Fix $p\geq 5$ an odd integer integer. Let $M_n$ be a uniform $p$-angulation with $n$ vertices and endowed with the uniform probability measure on its vertices. We prove that, there exists $C_p\in \mathbb{R}_+$ such that, after rescaling…

A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables $(X_k)_{k\geq1}$, there exists a probability measure $\mu$ on the Borel sets of $[0,1]$ such that $\bar X_n =…

Motivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random vectors which arise organically in the study of random clique complexes. These are: (1) the…

Our main contribution is a concentration inequality for the symmetric volume difference of a $ C^2 $ convex body with positive Gaussian curvature and a circumscribed random polytope with a restricted number of facets, for any probability…

We introduce a modification of the generalized P\'olya urn model containing two urns and we study the number of balls $B_j(n)$ of a given color $j\in\{1,\ldots,J\}$, $J\in\mathbb{N}$ added to the urns after $n$ draws. We provide sufficient…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

Let $\eta_i$, $i\ge 1$, be a sequence of independent and identically distributed random variables with finite third moment, and let $\Delta_n$ be the total variation distance between the distribution of $S_n:=\sum_{i=1}^n\eta_i$ and the…

We introduce a multi-colour multi-urn generalisation of the Bernoulli-Laplace urn model, consisting of $d$ urns, $m$ colours, and $dmn$ balls, with $dn$ balls of each colour and $mn$ balls in each urn. At each step, one ball is drawn…

We study the singular values (and Lyapunov exponents) for products of $N$ independent $n\times n$ random matrices with i.i.d. entries. Such matrix products have been extensively analyzed using free probability, which applies when $n\to…

Let $S_{n}$ be a sum of independent identically distribution random variables with finite first moment and $h_{M}$ be a call function defined by $g_{M}(x)=\max\{x-M,0\}$ for $x\in\mathbb{R}$, $M>0$. In this paper, we assume the random…

Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…

In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…