Asymptotic behaviour of a tagged particle in an inhomogeneous zero-range process
A spatially inhomogeneous zero-range jump process in \(\mathbb Z^d\) is investigated. The jumps are described by a symmetric random walk with the rate depending on the number of particles at \(x\in \mathbb Z^d\) and also on the site \(x\) itself. Roughly speaking, the main result states that the process describing the behaviour of a tagged particle, when rescaling the space by \(\frac {1}{\varepsilon}\) and the time by \(\frac {1}{\varepsilon ^2}\), tends to a diffusion on the \(d\)-dimensional torus when \(\varepsilon \) tends to zero. Ergodicity of some auxiliary Markov processes is used to deduce that a weak limit of the rescaled processes is the solution of a suitable martingale problem.
scientific article; zbMATH DE number 1364505
scientific article