Two-Sided Infinite Systems of Competing Brownian Particles

Sarantsev, Andrey

doi:10.1051/ps/2017013

Sarantsev, Andrey ¹

¹ Department of Statistics and Applied Probability, University of California, Santa BarbaraUSA

ESAIM: Probability and Statistics, Tome 21 (2017), pp. 317-349.

Résumé

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.

Reçu le : 2017-02-10
Accepté le : 2017-07-20

MR Zbl

DOI : 10.1051/ps/2017013

Classification : 60J60, 60J55, 60J65, 60H10, 60K35
Mots clés : Competing Brownian particles, gap process, weak convergence, stationary distribution, named particles, ranked particles, stochastic domination, interacting particle systems

Affiliations des auteurs :

Sarantsev, Andrey ¹

¹ Department of Statistics and Applied Probability, University of California, Santa BarbaraUSA

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Sarantsev, Andrey. Two-Sided Infinite Systems of Competing Brownian Particles. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 317-349. doi : 10.1051/ps/2017013. http://www.numdam.org/articles/10.1051/ps/2017013/

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