A Note on the Diffusive Scaling Limit for a Class of Linear Systems
Nobuo Yoshida (Kyoto University)
Abstract
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [NY09a] can be extended to wider class of models so that it covers the cases of potlatch/smoothing processes.
Full Text: Download PDF | View PDF online (requires PDF plugin)
Pages: 68-78
Publication Date: February 24, 2010
DOI: 10.1214/ECP.v15-1530
References
- Griffeath, David. The binary contact path process. Ann. Probab. 11 (1983), no. 3, 692--705. MR0704556 (85b:60097)
- Holley, Richard; Liggett, Thomas M. Generalized potlatch and smoothing processes. Z. Wahrsch. Verw. Gebiete 55 (1981), no. 2, 165--195. MR0608015 (82i:60176)
- Liggett, Thomas M. Interacting particle systems.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231 (86e:60089)
- Liggett, Thomas M.; Spitzer, Frank. Ergodic theorems for coupled random walks and other systems with locally interacting components. Z. Wahrsch. Verw. Gebiete 56 (1981), no. 4, 443--468. MR0621659 (82h:60193)
- Nagahata, Yukio; Yoshida, Nobuo. Central limit theorem for a class of linear systems. Electron. J. Probab. 14 (2009), no. 34, 960--977. MR2506122
- Nagahata, Yukio; Yoshida, Nobuo. Central limit theorem for a class of linear systems. Electron. J. Probab. 14 (2009), no. 34, 960--977. MR2506122
- Spitzer, Frank. Infinite systems with locally interacting components. Ann. Probab. 9 (1981), no. 3, 349--364. MR0614623 (82j:60186)
- Walters, Peter. An introduction to ergodic theory.Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. ISBN: 0-387-90599-5 MR0648108 (84e:28017)
This work is licensed under a Creative Commons Attribution 3.0 License.