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On the critical infection rate of the one-dimensional basic contact process: numerical results

Published online by Cambridge University Press:  14 July 2016

Herbert Ziezold*
Affiliation:
Gesamthochschule Kassel
Christian Grillenberger*
Affiliation:
Gesamthochschule Kassel
*
Postal address: Gesamthochschule Kassel, FB 17 Mathematik, Postf. 101380, 3500 Kassel, W. Germany.
Postal address: Gesamthochschule Kassel, FB 17 Mathematik, Postf. 101380, 3500 Kassel, W. Germany.

Abstract

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1988 

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