Abstract
We study the number
The proof relies on the introduction of adapted sequences of regenerating times, on subadditive arguments and on the properties of the coupled zone in supercritical oriented percolation. This global convergence result can be deepened to give directional limits and can be extended to more general random linear recursion equations known as linear stochastic evolutions.
Citation
Olivier Garet. Jean-Baptiste Gouéré. Régine Marchand. "The number of open paths in oriented percolation." Ann. Probab. 45 (6A) 4071 - 4100, November 2017. https://doi.org/10.1214/16-AOP1158
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