Modeling flocks and prices: Jumping particles with an attractive interaction

Balázs, Márton and Rácz, M. Z. and Tóth, Bálint (2014) Modeling flocks and prices: Jumping particles with an attractive interaction. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 50 (2). pp. 425-454. ISSN 0246-0203

Preview

Text 1108.2436.pdf Available under License Creative Commons Attribution. Download (398kB) | Preview

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.

Actions (login required)

Edit Item