Scaling Limit of Two-component Interacting Brownian Motions

2015/10/16 by Insuk Seo, Seo, Insuk · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1510.04776

openalex publication_date 2015/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents our study of the asymptotic behavior of a two-component system of Brownian motions undergoing certain singular interactions. In particular, the system is a combination of two different types of particles and the mechanical properties and interaction parameters depend on the corresponding type of particles. We prove that the hydrodynamic limit of the empirical densities of two types is the solution of a certain quasi-linear parabolic partial differential equation known as the Maxwell-Stefan equation.

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