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Convergence in distribution for subcritical 2D oriented percolation seen from its rightmost point

Abstract

We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.
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Dates and versions

hal-01113350 , version 1 (08-06-2023)

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E. D. Andjel. Convergence in distribution for subcritical 2D oriented percolation seen from its rightmost point. 2023. ⟨hal-01113350⟩
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