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.
Publié le : 1974-08-14
Classification:
Random Stirring,
measure-preserving bijection,
infinite particle system,
invariant measure,
reserve process,
$m$-recurrent Markov process,
convergence to equilibrium,
60K35,
28A65,
60B10
@article{1176996605,
author = {Lee, Wang Chung},
title = {Random Stirring of the Real Line},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 580-592},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996605}
}
Lee, Wang Chung. Random Stirring of the Real Line. Ann. Probab., Tome 2 (1974) no. 6, pp. 580-592. http://gdmltest.u-ga.fr/item/1176996605/