Modeling flocks and prices: Jumping particles with an attractive interaction

Márton Balázs, Miklós Z. Rácz, Bálint Tóth

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles goes to infinity, the evolution of the system is described by a mean field equation that exhibits traveling wave solutions. A connection to extreme value statistics is also provided.

Original languageEnglish
Pages (from-to)425-454
Number of pages30
JournalAnnales de l'Institut Henri Poincaré (B) Probabilités et Statistiques
Volume50
Issue number2
DOIs
Publication statusPublished - 2014

Keywords

  • Center of mass
  • Competing particles
  • Extreme value statistics
  • Fluid limit
  • Mean field evolution
  • Traveling wave

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