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 $\gamma \uparrow \pi/4.$ Our principal results show that the convergence of the critical probability to 1 is polynomial as $d\to \infty$ and $\gamma \uparrow \pi/4.$ In addition, we identify the correct order of this polynomial convergence and in $d=1$ we also obtain the correct prefactor.
Citation
Alexander Drewitz. Michael Scheutzow. Maite Wilke-Berenguer. "Asymptotics for Lipschitz percolation above tilted planes." Electron. J. Probab. 20 1 - 23, 2015. https://doi.org/10.1214/EJP.v20-4251
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