Fluid limit for the coarsening phase of the condensing zero-range process

Inés Armendáriz; Johel Beltrán; Daniela Cuesta; Milton Jara

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arXiv · 2302.05497

Fluid limit for the coarsening phase of the condensing zero-range process

Inés Armendáriz·Johel Beltrán·Daniela Cuesta·Milton Jara

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Abstract

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.

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Inés Armendáriz, Johel Beltrán, Daniela Cuesta, Milton Jara. 2023-02-10. Fluid limit for the coarsening phase of the condensing zero-range process. https://arxiv.org/abs/2302.05497

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