2017/11/30 by Gioia Carinci, Cristian Giardinà, Carinci, Gioia +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1711.11283
openalex publication_date 2017/11/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider two particles performing continuous-time nearest neighbor random\nwalk on mathbb Z and interacting with each other when they are at\nneighboring positions. Typical examples are two particles in the partial\nexclusion process or in the inclusion process. We provide an exact formula for\nthe Laplace-Fourier transform of the transition probabilities of the\ntwo-particle dynamics. From this we derive a general scaling limit result,\nwhich shows that the possible scaling limits are coalescing Brownian motions,\nreflected Brownian motions, and sticky Brownian motions. In particle systems\nwith duality, the solution of the dynamics of two dual particles provides\nrelevant information. We apply the exact formula to the the symmetric inclusion\nprocess, that is self-dual, in the condensation regime. We thus obtain two\nresults. First, by computing the time-dependent covariance of the particle\noccupation number at two lattice sites we characterize the time-dependent\ncoarsening in infinite volume when the process is started from a homogeneous\nproduct measure. Second, we identify the limiting variance of the density field\nin the diffusive scaling limit, relating it to the local time of sticky\nBrownian motion.\n