Asymptotics for Lipschitz percolation above tilted planes

Alexander Drewitz; Michael Scheutzow; Maite Wilke-Berenguer

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arXiv · 1504.05405

Asymptotics for Lipschitz percolation above tilted planes

Alexander Drewitz·Michael Scheutzow·Maite Wilke-Berenguer

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Abstract

We consider Lipschitz percolation in $d+1$ dimensions above planes tilted by an angle $\gamma$ along one or several coordinate axes. In particular, we are interested in the asymptotics of the critical probability as $d \to \infty$ as well as $\gamma \to \pi/4.$ Our principal results show that the convergence of the critical probability to 1 is polynomial as $d\to \infty$ and $\gamma \to \pi/4.$ In addition, we identify the correct order of this polynomial convergence and in $d=1$ we also obtain the correct prefactor.

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Alexander Drewitz, Michael Scheutzow, Maite Wilke-Berenguer. 2015-04-21. Asymptotics for Lipschitz percolation above tilted planes. https://arxiv.org/abs/1504.05405

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