Modeling flocks and prices: Jumping particles with an attractive interaction

Márton Balázs; Miklós Z. Rácz; Bálint Tóth

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 425-454
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Balázs, Márton, Rácz, Miklós Z., and Tóth, Bálint. "Modeling flocks and prices: Jumping particles with an attractive interaction." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 425-454. <http://eudml.org/doc/272089>.

@article{Balázs2014,
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.},
author = {Balázs, Márton, Rácz, Miklós Z., Tóth, Bálint},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {competing particles; center of mass; mean field evolution; traveling wave; fluid limit; extreme value statistics},
language = {eng},
number = {2},
pages = {425-454},
publisher = {Gauthier-Villars},
title = {Modeling flocks and prices: Jumping particles with an attractive interaction},
url = {http://eudml.org/doc/272089},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Balázs, Márton
AU - Rácz, Miklós Z.
AU - Tóth, Bálint
TI - Modeling flocks and prices: Jumping particles with an attractive interaction
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 425
EP - 454
AB - 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.
LA - eng
KW - competing particles; center of mass; mean field evolution; traveling wave; fluid limit; extreme value statistics
UR - http://eudml.org/doc/272089
ER -

References

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