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IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 43 (2010) 025001 (10pp) doi:10.1088/1751-8113/43/2/025001
 

Summary: IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
J. Phys. A: Math. Theor. 43 (2010) 025001 (10pp) doi:10.1088/1751-8113/43/2/025001
Empires and percolation: stochastic merging of
adjacent regions
D J Aldous1,2
, J R Ong and W Zhou
Department of Statistics, 367 Evans Hall # 3860, U.C. Berkeley, CA 94720, USA
E-mail: aldous@stat.berkeley.edu
Received 11 October 2009, in final form 5 November 2009
Published 10 December 2009
Online at stacks.iop.org/JPhysA/43/025001
Abstract
We introduce a stochastic model in which adjacent planar regions A, B merge
stochastically at some rate (A, B) and observe analogies with the well-studied
topics of mean-field coagulation and of bond percolation. Do infinite regions
appear in finite time? We give a simple condition on for this hegemony
property to hold, and another simple condition for it to not hold, but there is a
large gap between these conditions, which includes the case (A, B) 1. For
this case, a non-rigorous analytic argument and simulations suggest hegemony.
PACS number: 64.60.ah

  

Source: Aldous, David J. - Department of Statistics, University of California at Berkeley

 

Collections: Mathematics