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The critical contact process seen from the right edge
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  • Published: September 1991

The critical contact process seen from the right edge

  • J. T. Cox1,
  • R. Durrett2 &
  • R. Schinazi1 

Probability Theory and Related Fields volume 87, pages 325–332 (1991)Cite this article

  • 88 Accesses

  • 5 Citations

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Summary

Durrett (1984) proved the existence of an invariant measure for the critical and supercritical contact process seen from the right edge. Galves and Presutti (1987) proved, in the supercritical case, that the invariant measure was unique, and convergence to it held starting in any semi-infinite initial state. We prove the same for the critical contact process. We also prove that the process starting with one particle, conditioned to survive until timet, converges to the unique invariant measure ast→∞.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, 13210, Syracuse, NY, USA

    J. T. Cox & R. Schinazi

  2. Department of Mathematics, Cornell University, 14853, Ithaca, NY, USA

    R. Durrett

Authors
  1. J. T. Cox
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  2. R. Durrett
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  3. R. Schinazi
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Additional information

Partially supported by the National Science Foundation

Partially supported by the National Science Foundation, the National Security Agency, and the Army Research Office through the Mathematical Sciences Institute at Cornell University

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Cite this article

Cox, J.T., Durrett, R. & Schinazi, R. The critical contact process seen from the right edge. Probab. Th. Rel. Fields 87, 325–332 (1991). https://doi.org/10.1007/BF01312213

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  • Received: 18 December 1989

  • Revised: 17 May 1990

  • Issue Date: September 1991

  • DOI: https://doi.org/10.1007/BF01312213

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Keywords

  • Stochastic Process
  • Probability Theory
  • Invariant Measure
  • Mathematical Biology
  • Contact Process
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