Related papers: P\'olya urns with immigration at random times
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
We show that for planar dispersing billiards the return times distribution is, in the limit, Poisson for metric balls almost everywhere w.r.t. the SRB measure. Since the Poincar\'e return map is piecewise smooth but becomes singular at the…
Inspired by the Japanese game Pachinko, we study simple (perfectly "inelastic" collisions) dynamics of a unit ball falling amidst point obstacles (pins) in the plane. A classic example is that a checkerboard grid of pins produces the…
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of…
Many axiomatic definitions of entropy, such as the R\'enyi entropy, of a random variable are closely related to the $\ell_{\alpha}$-norm of its probability distribution. This study considers probability distributions on finite sets, and…
We study constrained selection sets of random closed sets defined on a non-atomic probability space. Given a random interval $Y=[y_L,y_U]$ and scalar constraints on the expectation or the median of admissible selections, we characterize the…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
The dynamics of random transitive delegations on a graph are of particular interest when viewed through the lens of an emerging voting paradigm, liquid democracy. This paradigm allows voters to choose between directly voting and…
Consider $n$ independent random numbers with a uniform distribution on $[0,1]$. The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is described by the Eulerian numbers. This is related to, but…
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…
Several differential equations usually appearing in mathematical physics are solved through a power series expansion, which reduces in solving difference equations. In this paper a probability problem is presented whose solution follows a…
Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
Early investigation of P\'{o}lya urns considered drawing balls one at a time. In the last two decades, several authors considered multiple drawing in each step, but mostly for schemes on two colors. In this manuscript, we consider multiple…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
Let $A$ be an $n \times n$ random matrix with iid entries over a finite field of order $q$. Suppose that the entries do not take values in any additive coset of the field with probability greater than $1 - \alpha$ for some fixed $0 < \alpha…
We review some facts, properties and applications of the urn of Hill, Lane and Sudderth, a paradigmatic model of stochastic process with memory where the urn evolution is as follows: consider an urn of given capacity, at each step a new…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
We investigate the profile of random P\'olya trees of size $n$ when only nodes of degree $d$ are counted in each level. It is shown that, as in the case where all nodes contribute to the profile, the suitably normalized profile process…
Suppose $k$ balls are dropped into $n$ boxes independently with uniform probability, where $n, k$ are large with ratio approximately equal to some positive real $\lambda$. The maximum box count has a counterintuitive behavior: first of all,…