Related papers: Functional limit theorems for the Polya and q-Poly…
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
We propose an approach to analyze the asymptotic behavior of P\'olya urns based on the contraction method. For this, a new combinatorial discrete time embedding of the evolution of the urn into random rooted trees is developed. A…
We study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha^{th}$ power $(\alpha >1)$ of the existing number of balls. We…
In this paper, we prove convergence and fluctuation results for measure-valued P\'olya processes (MVPPs, also known as P\'olya urns with infinitely-many colours). Our convergence results hold almost surely and in $L^2$, under assumptions…
We establish Central Limit Theorems for the volumes of intersections of $B_{p}^n$ (the unit ball of $\ell_p^n$) with uniform random subspaces of codimension $d$ for fixed $d$ and $n\to \infty$. As a corollary we obtain higher order…
Drawing (a multiset of) coloured balls from an urn is one of the most basic models in discrete probability theory. Three modes of drawing are commonly distinguished: multinomial (draw-replace), hypergeometric (draw-delete), and Polya…
We study a class of unbalanced constant-differentials P\'olya processes on white and blue balls. We show that the number of white balls, the number of blue balls, and the total number of balls, when appropriately scaled, all converge in…
Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
In a balls-in-bins process with feedback, balls are sequentially thrown into bins so that the probability that a bin with n balls obtains the next ball is proportional to f(n) for some function f. A commonly studied case where there are two…
We propose a method of detecting a phase transition in a generalized P\'olya urn in an information cascade experiment. The method is based on the asymptotic behavior of the correlation $C(t)$ between the first subject's choice and the…
We prove a central limit theorem applicable to one dimensional stochastic approximation algorithms that converge to a point where the error terms of the algorithm do not vanish. We show how this applies to a certain class of these…
We define and prove limit results for a class of dominant P\'olya sequences, which are randomly reinforced urn processes with color-specific random weights and unbounded number of possible colors. Under fairly mild assumptions on the…
We prove that for q>=1, there exists r(q)<1 such that for p>r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure phi_{p,q} on Z^d, d>=2.…
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 $\mathbb{B}_p^N$…
The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this…
Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1<p<d$. Upper and lower bounds are obtained for the product of $p$-capacity and powers of the $q$-torsional rigidity over the collection of all…
Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…
Consider a stationary Poisson process of horospheres in a $d$-dimensional hyperbolic space. In the focus of this note is the total surface area these random horospheres induce in a sequence of balls of growing radius $R$. The main result is…