2020/04/01 by Alexander Stolyar, Stolyar, Alexander
Mathematics · Physics and Astronomy · #60K25 #60K35 #90B15 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2004.00177
openalex publication_date 2020/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that n particles move forward on the real line. Specifically, each particle "jumps forward" at some time points, with the instantaneous rate of jumps given by a decreasing function of the particle's location quantile within the overall distribution of particle locations. A mean-field model describes the evolution of the particles' distribution, when n is large. It is essentially a solution to an integro-differential equation within a certain class. Our main results concern the existence and uniqueness of -- and attraction to -- mean-field models which are traveling waves, under general conditions on the jump-rate function and the jump-size distribution.