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Exact formulas for two interacting particles and applications in particle systems with duality. (arXiv:1711.11283v1 [math.PR])
来源于:arXiv
We consider two particles performing continuous-time nearest neighbor random
walk on $\mathbb Z$ and interacting with each other when they are at
neighboring positions. Typical examples are two particles in the partial
exclusion process or in the inclusion process. We provide an exact formula for
the Laplace-Fourier transform of the transition probabilities of the
two-particle dynamics. From this we derive a general scaling limit result,
which shows that the possible scaling limits are coalescing Brownian motions,
reflected Brownian motions, and sticky Brownian motions. In particle systems
with duality, the solution of the dynamics of two dual particles provides
relevant information. We apply the exact formula to the the symmetric inclusion
process, that is self-dual, in the condensation regime. We thus obtain two
results. First, by computing the time-dependent covariance of the particle
occupation number at two lattice sites we characterize the time-dependent
coarsening in infinite vo 查看全文>>