Volume 21, 2017
|Page(s)||317 - 349|
|Published online||12 December 2017|
Two-Sided Infinite Systems of Competing Brownian Particles
Department of Statistics and Applied Probability, University of California, Santa Barbara, USA.
Received: 10 February 2017
Revised: 13 June 2017
Accepted: 20 July 2017
Two-sided infinite systems of Brownian particles with rank-dependent dynamics, indexed by all integers, exhibit different properties from their one-sided infinite counterparts, indexed by positive integers, and from finite systems. Consider the gap process, which is formed by spacings between adjacent particles. In stark contrast with finite and one-sided infinite systems, two-sided infinite systems can have one- or two-parameter family of stationary gap distributions, or the gap process weakly converging to zero as time goes to infinity.
Mathematics Subject Classification: 60J60 / 60J55 / 60J65 / 60H10 / 60K35
Key words: Competing Brownian particles / gap process / weak convergence / stationary distribution / named particles / ranked particles / stochastic domination / interacting particle systems
© EDP Sciences, SMAI, 2017
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