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Approximations finies de la mesure invariante do processus de contact sur-critique vu par la première particule
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  • Published: December 1989

Approximations finies de la mesure invariante do processus de contact sur-critique vu par la première particule

  • Antonio Galves1 &
  • Rinaldo Schinazi1 

Probability Theory and Related Fields volume 83, pages 435–445 (1989)Cite this article

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Summary

For each integern≧1 we consider the contact process as seen from the first particle and we do not allow the process to disappear or to have more thann particles. We prove that the invariant probability of this process converges to a limit whenn goes to infinity. This limit is exactly the invariant probability measure of the usual contact process as seen from the first particle. Durrett [1] has proven the existence of this probability and Galves and Presutti [3] have shown its uniqueness. We get here a new proof of the existence of this probability and a complete convergence theorem for finite and infinite initial configurations.

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Bibliographie

  1. Durrett, R.: Oriented Percolation in two dimensions. Ann. Probab.12, 999–1040 (1984)

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  2. Durrett, R., Griffeath, D.: Supercritical contact processes on Z. Ann. Probab.11, 1–15 (1983)

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  3. Galves, A., Presutti, E.: Edge fluctuations for the one dimensional supercritical contact process. Ann. Probab.15, 1131–1145 (1987)

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  4. Galves, A., Presutti, E.: Travelling wave structure of the one dimensional contact process. Stochastic Processes Appl.25, 153–163 (1987)

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  5. Holley, R.: An ergodic theorem for interacting particle systems with attractive interactions. Z. Wahrscheinlichkeitstheor. Verw. Geb.24, 325–334 (1972)

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  6. Liggett, T.: Interacting particles systems. Berlin Heidelberg New York: Springer 1985

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Ag. Iguatemi, Caixa Postal 20570, Cep 01498, São Paulo, S.P, Brasil

    Antonio Galves & Rinaldo Schinazi

Authors
  1. Antonio Galves
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  2. Rinaldo Schinazi
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A.G bénéficie du support financier du C.N.P.q bourse 301301/79

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Galves, A., Schinazi, R. Approximations finies de la mesure invariante do processus de contact sur-critique vu par la première particule. Probab. Th. Rel. Fields 83, 435–445 (1989). https://doi.org/10.1007/BF01845698

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  • Received: 21 June 1988

  • Issue Date: December 1989

  • DOI: https://doi.org/10.1007/BF01845698

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