Related papers: A new method for computing the expected hitting ti…
This is the second part of a two-part investigation. We continue the study of a class of balanced urn schemes on balls of two colors (white and black). At each drawing, a sample of size $m\ge 1$ is drawn from the urn and ball addition rules…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
We show that the recently proposed interacting Ehrenfest M-urn model at equilibrium can be exactly mapped to a mean-field M-state Potts model. By exploiting this correspondence, we show that the M-state Potts model with M >= 3, with…
We consider a continuous-time Ehrenfest model defined over the integers from -N to N, and subject to catastrophes occurring at constant rate. The effect of each catastrophe instantaneously resets the process to state 0. We investigate both…
This work addresses potential theoretic questions for the standard nearest neighbor random walk on the hypercube $\{-1,+1\}^N$. For a large class of subsets $A\subset\{-1,+1\}^N$ we give precise estimates for the harmonic measure of $A$,…
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…
Consider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn…
In this paper, we consider a multi-drawing urn model with random addition. At each discrete time step, we draw a sample of m balls. According to the composition of the drawn colors, we return the balls together with a random number of balls…
The recently proposed Ehrenfest M-urn model with interactions on a ring is considered as a paradigm model which can exhibit a variety of distinct nonequilibrium steady states. Unlike the previous three-urn model on a ring which consists of…
I present a generalization of the Ehrenfest urn model that is aimed at simulating the approach to equilibrium in a dilute gas. The present model differs from the original one in two respects: 1) the two boxes have different volumes and are…
Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of…
An urn scheme is a probabilistic model in which balls are placed into urns sequentially and independently of each other. All balls share the same probability distribution for hitting the urns. In the simplest case, there is a finite number…
We study an urn process containing red and blue balls and two different strategies to reinforce the urn. Namely, a generalized P\'olya-type strategy versus an i.i.d. one. At each step, one of the two reinforcement strategies is chosen by…
This is a research endeavor in two parts. We study a class of balanced urn schemes on balls of two colours (say white and black). At each drawing, a sample of size $m\ge 1$ is drawn from the urn, and ball addition rules are applied. We…
Consider throwing $n$ balls at random into $m$ urns, each ball landing in urn $i$ with probability $p_i$. Let $S$ be the resulting number of singletons, i.e., urns containing just one ball. We give an error bound for the Kolmogorov distance…
In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination…
Consider an urn model where at each step one of $q$ colors is sampled according to some probability distribution and a ball of that color is placed in an urn. The distribution of assigning balls to urns may depend on the color of the ball.…
This paper considers a two-color, single-draw urn model with two types of balls, denoted type $1$ and type $2$, with initial counts $Y^1_0\in N^+$ and $Y^2_0\in N^+$, respectively. At each discrete time step, a ball is drawn uniformly at…
We consider multicolor urn models with multiple drawings. An urn model is called linear if the conditional expected value of the urn composition at time $n$ is a linear function of the composition at time $n-1$. For four different sampling…
We study real-space condensation phenomena in a type of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We here study a stochastic process in the Ehrenfest class, i.e., particles in a site…