First Passage Properties of the Polya Urn Process

Details First Passage Properties of the Polya Urn Process First Passage Properties of the Polya Urn Process

2010-05-05

arxiv.org/abs/1005.0867v1

J. Stat. Mech. P07009 (2010)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures

Scientific paper

10.1088/1742-5468/2010/07/P07009

We study first passage statistics of the Polya urn model. In this random process, the urn contains two types of balls. In each step, one ball is drawn randomly from the urn, and subsequently placed back into the urn together with an additional ball of the same type. We derive the probability G_n that the two types of balls are equal in number, for the first time, when there is a total of 2n balls. This first passage probability decays algebraically, G_n ~ n^{-2}, when n is large. We also derive the probability that a tie ever happens. This probability is between zero and one, so that a tie may occur in some realizations but not in others. The likelihood of a tie is appreciable only if the initial difference in the number balls is of the order of the square-root of the total number of balls.

Affiliated with

Also associated with

No associations

Rating

First Passage Properties of the Polya Urn Process does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with First Passage Properties of the Polya Urn Process, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and First Passage Properties of the Polya Urn Process will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25486