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August, 1974 Random Stirring of the Real Line
Wang Chung Lee
Ann. Probab. 2(4): 580-592 (August, 1974). DOI: 10.1214/aop/1176996605


Random stirring of the real line $R_1$ is defined. This notion is derived from a generalization of the nearest-neighbor simple exclusion model on the one-dimensional lattices discussed by Spitzer and by Harris. Under the random stirring, the motion of an infinite particle system is Markovian and has a Poisson process as an invariant probability measure. An ergodic theorem is established concerning the convergence of a system to a Poisson process.


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Wang Chung Lee. "Random Stirring of the Real Line." Ann. Probab. 2 (4) 580 - 592, August, 1974.


Published: August, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0288.60094
MathSciNet: MR362563
Digital Object Identifier: 10.1214/aop/1176996605

Primary: 60K35
Secondary: 28A65 , 60B10

Keywords: $m$-recurrent Markov process , Convergence to equilibrium , Infinite particle system , invariant measure , measure-preserving bijection , Random Stirring , reserve process

Rights: Copyright © 1974 Institute of Mathematical Statistics

Vol.2 • No. 4 • August, 1974
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