Celebratio Mathematica — Liggett — Complete Bibliography

Complete Bibliography

Works connected to Petre Tăutu

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T. M. Liggett: “Interacting Markov processes,” pp. 145–156 in Biological growth and spread: Mathematical theories and applications (Heidelberg, Germany, 16–21 July 1979). Edited by W. Jäger, H. Rost, and P. Tăutu. Lecture Notes in Biomathematics 38. Springer (Berlin), 1980. MR 609355 Zbl 0457.60080 incollection

Hermann Rost	Related
Willi Jäger	Related
Petre Tăutu	Related

T. M. Liggett: “Nearest particle systems: Results and open problems,” pp. 200–215 in Stochastic spatial processes: Mathematical theories and biological applications (Heidelberg, Germany, 10–14 September 1984). Edited by P. Tautu. Lecture Notes in Mathematics 1212. Springer (Berlin), 1986. MR 877777 Zbl 0603.60094 incollection

Nearest particle systems are certain continuous time Markov processes on \( X = \{O,1\}^\mathbb{Z} \) where \( \mathbb{Z} \) is the set of integers). Flips occur from zero to one and from one to zero at each site. The characteristic property of these systems is that the rate at which a coordinate flips depends on the rest of the configuration only through the distances to the nearest sites to the right and left which have the value one. These processes were introduced by Spitzer [1977], and have been the subject of a number of papers since then. A substantial theory of these processes has been developed, but a number of open problems still remain. This paper presents an overview of the theory as it stands today, and a description of some of the more important open problems which should be addressed. No detailed proofs will be provided here, but in many cases the main ideas of the proof will be given. Complete proofs can be found in the original papers, or in [Liggett 1985, Chapter VII].