Bin sizes in time-inhomogeneous infinite Polya processes

publisher: Elsevier articletitle: Bin sizes in time-inhomogeneous infinite Polya processes journaltitle: Statistics & Probability Letters articlelink: http://dx.doi.org/10.1016/j.spl.2016.02.010 content_type: article copyright: Copyright © 2016 Elsevier B.V. All rights reserved

Limiting shapes of birth-and-death processes on young diagrams

Abstract We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rost's totally asymmetric particle model (in discrete time), Simon's urban growth model, and Moran's infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures