Phases in the two-color tenable zero-balanced Pólya process

Joshua Sparks and Hosam M. Mahmoud

Statistics & Probability Letters, 2013, vol. 83, issue 1, 265-271

Abstract: The Pólya process is obtained by embedding the usual (discrete-time) Pólya urn scheme in continuous time. We study the class of tenable Pólya processes of white and blue balls with zero balance (no change in n, the total number of balls, over time). This class includes the (continuous-time) Ehrenfest process and the (continuous-time) Coupon Collector’s process. We look at the composition of the urn at time tn (dependent on n). We identify a critical phase of tn at the edges of which phase transitions occur. In the subcritical phase, under proper scaling the number of white balls is concentrated around a constant. In the critical phase, we have sufficient variability for an asymptotic normal distribution to be in effect. In this phase, the influence of the initial conditions is still somewhat pronounced. Beyond the critical phase, the urn is very well mixed with an asymptotic normal distribution, in which all initial conditions wither away. The results are obtained by an analytic approach utilizing partial differential equations.

Keywords: Urn; Pólya urn; Pólya process; Phase transition; Partial differential equation (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715212003252
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:83:y:2013:i:1:p:265-271

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2012.08.020

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().