## Abstract

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 language | English (US) |
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Pages (from-to) | 245-274 |

Number of pages | 30 |

Journal | Advances in Applied Probability |

Volume | 55 |

Issue number | 1 |

DOIs | |

State | Published - Mar 27 2023 |

## Keywords

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

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics