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Estimating the critical values of stochastic growth models

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

L. Buttell ,
J. T. Cox  and
R. Durrett
L. Buttell*
Affiliation:
Cornell University
J. T. Cox*
Affiliation:
Syracuse University
R. Durrett*
Affiliation:
Cornell University
*
∗ Postal address: Department of Ecology and Systematics, Cornell University, Ithaca, NY 14853, USA.
∗∗Postal address: Department of Mathematics, Syracuse University, Syracuse, NY 13244, U.S.A.
∗∗∗ Postal address: Department of Mathematics, Cornell University, Ithaca, NY 14853–7901, USA.
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Abstract

Interacting particle systems provide an attractive framework for modelling the growth and spread of biological populations and diseases. One problem with their use in applications is that in most cases the existing information about their critical values and equilibrium densities is too crude to be useful. In this paper we describe a method for estimating these quantities that does not require very much computer time and produces fairly accurate results.

Keywords

CONTACT PROCESSCRITICAL VALUES

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 455 - 461
Copyright
Copyright © Applied Probability Trust 1993 

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References

Brower, R. C., Furman, M. A. and Moshe, M. (1978) Critical exponents for the Reggeon quantum spin model. Phys. Lett. 76B, 213–219.CrossRefGoogle Scholar
Cardy, J. L. and Sugar, R. L. (1980) Directed percolation and Reggeon field theory. J. Phys. A 13, L423–L427.Google Scholar
Cox, J. T. and Durrett, R. (1991) Nonlinear voter models. To appear in a volume in honor of Frank Spitzer. Birkhauser, Boston.Google Scholar
Dickman, R. and Burschka, M. A. (1988) Nonequilibrium critical poisoning in a single-species model. Phys. Lett. A 127, 132–137.Google Scholar
Durrett, R. (1988) Lecture Notes on Particle Systems and Percolation. Wadsworth, Pacific Grove, CA.Google Scholar
Grassberger, P. (1982) On phase transitions in Schögl's second model. Z. Phys. B 47, 365–374.Google Scholar
Grassberger, P. and De La Torre, A. (1979) Reggeon field theory (Schögl's first model) on a lattice: Monte Carlo calculation of critical behaviour. Ann. Phys. 122, 373–396.CrossRefGoogle Scholar
Holley, R. A. and Liggett, T. M. (1978) The survival of contact processes. Ann. Prob. 6, 198–206.Google Scholar
Janssen, H. K. (1981) On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state. Z. Phys. B 42, 151–154.CrossRefGoogle Scholar
Liggett, T. M. (1985) Interacting Particle Systems. Springer-Verlag, New York.Google Scholar
Liggett, T. M. (1991) The periodic threshold contact process. To appear in a volume in honor of Frank Spitzer, Birkhauser, Boston.CrossRefGoogle Scholar