The critical contact process seen from the right edge
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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→∞.
KeywordsStochastic Process Probability Theory Invariant Measure Mathematical Biology Contact Process
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