Large-scale behavior of a particle system with mean-field interaction: Traveling wave solutions

Research output: Contribution to journalArticlepeer-review


We use probabilistic methods to study properties of mean-field models, which arise 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.

Original languageEnglish (US)
Pages (from-to)245-274
Number of pages30
JournalAdvances in Applied Probability
Issue number1
StatePublished - Mar 27 2023


  • Particle system
  • asymptotic behavior
  • distributed system synchronization
  • mean-field model dynamics

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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