2023/02/10 by Inés Armendáriz, J. Beltrán, Armendáriz, Inés +5
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2302.05497
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is described by a piecewise linear trajectory in the simplex indexed by the sites. The linear coefficients are determined by the trace process of the underlying random walk on the subset of non-empty sites, and the trajectory reaches an absorbing configuration in finite time. A boundary of the simplex is called absorbing for the fluid limit if a trajectory started at a configuration in the boundary remains in it for all times. We identify the set of absorbing configurations and characterize the absorbing boundaries.