Brownian Particles with Rank‐Dependent Drifts: Out‐of‐Equilibrium Behavior

Autor:	Vladas Sidoravicius, Andrey Sarantsev, Amir Dembo, Manuel Cabezas
Rok vydání:	2019
Předmět:	Rank (linear algebra) Applied Mathematics General Mathematics Equilibrium behavior Mathematical analysis Convergence (routing) Particle Countable set Constant (mathematics) Trajectory (fluid mechanics) Brownian motion Mathematics
Zdroj:	Communications on Pure and Applied Mathematics. 72:1424-1458
ISSN:	1097-0312 0010-3640
Popis:	We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost particle gets a constant drift to the right, we derive and solve the corresponding one- sided Stefan (free-boundary) equations. Via this solution we explicitly determine the limiting particle-density profile as well as the asymptotic trajectory of the leftmost particle. While doing so we further establish stochastic domination and convergence to equilibrium results for the vector of relative spacings among the leading particles.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::088af6f143c75ab4d27dda9f8b5fcf81 https://doi.org/10.1002/cpa.21825 Zobrazit plný text záznamu Plný text