Related papers: Time-dependent balls and bins model with positive …

Consider a balls-in-bins process in which each new ball goes into a given bin with probability proportional to f(n), where n is the number of balls currently in the bin and f is a fixed positive function. It is known that these so-called…

Balls-in-bins models describe a random sequential allocation of infinitely many balls into a finite number of bins. In these models a ball is placed into a bin with probability proportional to a given function (feedback function), which…

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…

Consider a generalized time-dependent P\'olya urn process defined as follows. Let $d\in \mathbb{N}$ be the number of urns/colors. At each time $n$, we distribute $\sigma_n$ balls randomly to the $d$ urns, proportionally to $f$, where $f$ is…

Imagine that there are two bins to which balls are added sequentially, and each incoming ball joins a bin with probability proportional to the p-th power of the number of balls already there. A general result says that if p>1/2, there…

Balls-and-bins games have been a wildly successful tool for modeling load balancing problems. In this paper, we study a new scenario, which we call the ball recycling game, defined as follows: Throw m balls into n bins i.i.d. according to a…

We consider a time-dependent version of a P\'olya urn containing black and white balls. At each time $n$ a ball is drawn from the urn at random and replaced in the urn along with $\sigma_n$ additional balls of the same colour. The…

We analyse the balls in bins process with feedback with primary focus on the power law feedback function $f(\omega)=\eta \omega^{\gamma}\,$, $\eta>0\,$ $\gamma \geq0\,$. Using the recursive solution to the master equation we find for power…

Generalized P\'olya urns with non-linear feedback are an established probabilistic model to describe the dynamics of growth processes with reinforcement, a generic example being competition of agents in evolving markets. It is well known…

We introduce and discuss a special type of feedback interacting urn model with deterministic interaction. This is a generalisation of the very well known Eggenberger and Polya (1923) urn model. In our model, balls are added to a particular…

Consider a model of $N$ independent, increasing $\mathbb{N}_0$-valued processes, with random, independent waiting times between jumps. It is known that there is either an emergent `leader', in which a single process possesses the maximal…

We propose a stochastic model of opinion exchange in networks. A finite set of agents is organized in a fixed network structure. There is a binary state of the world and each agent receives a private signal on the state. We model beliefs as…

In the classical balls-and-bins model, $m$ balls are allocated into $n$ bins one by one uniformly at random. In this note, we consider the $d$-thinning variant of this model, in which the process is regulated in an on-line fashion as…

Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability…

We revisit the random allocation model in which $n$ balls are independently placed into $N$ boxes with probabilities $q_1,\ldots,q_N$. A classical asymptotic result due to Kolchin, Sevastyanov, and Chistyakov for the expectations,…

We study the number of white balls in a classical P\'olya urn model with the additional feature that, at random times, a black ball is added to the urn. The number of draws between these random times are i.i.d. and, under certain moment…

Suppose that there are n bins, and balls arrive in a Poisson process at rate \lambda n, where \lambda >0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is placed into one with least load. Balls have…

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…

Consider the following process whereby $n$ balls are distributed into $k$ bins. Repeatedly, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. Will Ma…

We study a P\'olya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n>0, choose a ball from the urn uniformly at random. With probability 1/2<p<1, return the ball to the urn along with…