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June, 1981 Infinite Systems with Locally Interacting Components
Frank Spitzer
Ann. Probab. 9(3): 349-364 (June, 1981). DOI: 10.1214/aop/1176994410


In 1963 Glauber analyzed a one dimensional model for magnetism. It was the first study of the Markovian time evolution of a system with infinitely many interacting components. In Section 1 it will be discussed in the light of recent progress in this field. The remaining Sections (2, 3, and 4) form an introduction to recent joint work with Thomas M. Liggett. They concern new types of systems where each component takes on a real value which fluctuates in a way depending linearly on the values of neighboring components. The ergodic theory for such systems with finitely many components is the subject of Section 2. The results suggest conjectures for the case of infinitely many components, stated in Section 3 and proved in the joint paper with T. Liggett (ibid.). Section 4 introduces another class of time evolutions whose ergodic behavior may be analyzed by similar methods.


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Frank Spitzer. "Infinite Systems with Locally Interacting Components." Ann. Probab. 9 (3) 349 - 364, June, 1981.


Published: June, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0462.60096
MathSciNet: MR614623
Digital Object Identifier: 10.1214/aop/1176994410

Primary: 60K35

Keywords: coupled random walks , Dual processes , equilibrium states , interacting particle systems

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • June, 1981
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