Quasi-stationary measures for conservative dynamics in the infinite lattice. (English) Zbl 1018.60092

The authors establish existence and qualitative properties of quasi-stationary measures for a class of conservative particle systems in a \(d\)-dimensional lattice. Their approach is based on showing that any limit point of certain Cesaro’s means is quasi-stationary provided reversibility of the initial condition.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
60J25 Continuous-time Markov processes on general state spaces
Full Text: DOI


[1] Andjel, E. (1982). Invariant measures for the zero range process. Ann. Probab. 10 525-547. · Zbl 0492.60096
[2] Arratia, R. (1985). Symmetric exclusion processes: a comparison inequality and a large deviation result. Ann. Probab. 13 53-61. · Zbl 0558.60075
[3] Asselah, A. and Dai Pra, P. (2000). First occurrence time of a large density fluctuation for a system of independent random walks. Ann. Inst. H. Poincaré Probab. Statist. 36 367-393. · Zbl 0982.60036
[4] Chow, Y. S. and Teicher, H. (1978). Probability Theory. Springer, New York. · Zbl 0399.60001
[5] De Masi, A. and Presutti, E. (1991). Mathematical methods for hydrodynamic limits. Lecture Notes in Math. 1501. Springer, Berlin. · Zbl 0754.60122
[6] Ferrari, P. A., Kesten H., Martinez S. and Picco P. (1995). Existence of quasi-stationary distributions: renewal dynamical approach. Ann. Probab. 23 501-521. · Zbl 0827.60061
[7] Keilson, J. (1979). Markov Chain Models: Rarity and Exponentiality. Springer, Berlin. · Zbl 0411.60068
[8] Lawler, G. (1991). Intersections of Random Walks. Birkhäuser, Boston. · Zbl 1228.60004
[9] Liggett, T. M. (1973). An infinite particle system with infinite range iteraction. Ann. Probab. 1 240-253. · Zbl 0264.60083
[10] Liggett, T. M. (1985). Interacting Particle Systems. Springer, New York. · Zbl 0559.60078
[11] Ma,M. and R öckner, M. (1992). Dirichlet Forms. Springer, Berlin. · Zbl 0786.60104
[12] Varadhan, S. R. S. (1994). Regularity of self-diffusion coefficient. Progr. Probab. 34 387-397. · Zbl 0822.60089
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.