2016/02/22 by J Cividini, J. Cividini, A. Kundu +5 · 2 citations
Mathematics · Physics and Astronomy · #Correlation #Correlation function (quantum field theory) #Function (biology) #Limit (mathematics) #Particle (ecology) #Position (finance) #Scaling #Stochastic processes and statistical mechanics #TRACER #Theoretical and Computational Physics #Variance (accounting) #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/2016/05/053212
24 pages, 11 figures
arxiv created 2016/02/22 · openalex publication_date 2016/05/26 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the effect of a single biased tracer particle in a bath of other particles performing the random average process (RAP) on an infinite line. We focus on the long time behavior of the mean and the fluctuations of the positions of the particles and also the correlations among them. In the long time t limit these quantities have well defined scaling forms and grow with time as . A differential equation for the scaling function associated with the correlation function is obtained and solved perturbatively around the solution for a symmetric tracer. Interestingly, when the tracer is totally asymmetric, further progress is enabled by the fact that the particles behind the tracer do not affect the motion of the particles in front of it, which leads in particular to an exact expression for the variance of the position of the tracer. Finally, the variance and correlations of the gaps between successive particles are also studied. Numerical simulations support our analytical results.