Asymptotic behaviour in the time synchronization model

Details Asymptotic behaviour in the time synchronization model Asymptotic behaviour in the time synchronization model

2012-01-10

arxiv.org/abs/1201.2141v1

Representation Theory, Dynamical Systems, and Asymptotic Combinatorics, AMS Translations - Series 2: Advances in the Mathemati

Physics

Mathematical Physics

16 pages; first published in Representation Theory, Dynamical Systems, and Asymptotic Combinatorics, AMS Translations - Series

Scientific paper

There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}\alpha_{ij}$. We discuss in details the initial desynchronization of this particle system, namely, we are interested in behaviour of the process when the total number of particles $N_1+N_2$ tends to infinity, the ratio $N_1/N_2$ is constant and the time $t>0$ is fixed.

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