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Limiting behavior of a one-dimensional system with long range interactions. (English) Zbl 0731.60094
Mathematics of random media, Proc. AMS-SIAM Summer Semin., Conf., Blacksburg/VA (USA) 1989, Lect. Appl. Math. 27, 31-40 (1991).
[For the entire collection see Zbl 0725.00015.]
The author reviews recent results on the limiting behaviour of the nearest particle system for large times, in particular survival vs. extinction, critical behaviour, invariant measures and rate of convergence.
60K35 Interacting random processes; statistical mechanics type models; percolation theory