Some properties of \(k\)-step exclusion processes
The author studies a generalization of the well-known simple exclusion process. Roughly speaking, the process evolves as follows. On each site, there is a clock that rings with exponential rate \(1\). The clocks at different sites are iid. If a particle is at present at site \(x\) when the clock associated to this site rings, then the particle occupies the first vacant site encountered in the sequence \((X_n)_{1\leq n \leq k}\), where \(\{X_n\}_n\) is a Markov chain starting from \(x\) (the Markov chain is assumed to be a random walk, or reversible and positive recurrent). If no empty site is encountered during these \(k\) attempts, then the movement is cancelled and the particle stays at \(x\). As in the original situation, the author studies the structure of the invariant measures, the law of large numbers for two classes of particles (the first class is the standard tagged one).
scientific article; zbMATH DE number 1370579