Urns with simultaneous drawing

Abstract

In classical urn models, one usually draws one ball with replacement at each time unit and then adds one ball of the same colour. Given a weight sequence $(w_k{)}_{k\in \mathbb{N}}$, the probability of drawing a ball of a certain colour is proportional to $w_k$ where $k$ is the number of balls of this colour. A classical result states that an urn fixates on one colour after a finite time if an only if ${\sum }_0^{\infty }{w}_k^{-1}<\infty$. In this paper we shall study the case when at each time unit we draw with replacement a number $d\in \mathbb{N}$ of balls and then add $d$ new balls of matching colours. The main goal is to prove that the result in the case of maximal interaction generalizes assuming in addition that $(w_k{)}_{k\in \mathbb{N}}$ is non-decreasing.

12 pages

References in corpus (2)

• A survey of random processes with reinforcement
• Interacting Urn Models

Cited by in corpus (1)

• Urn models with random multiple drawing and random addition