## Electronic Journal of Probability

### Asymptotics for Lipschitz percolation above tilted planes

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 117, 23 pp.

Dates
Accepted: 1 November 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067223

Digital Object Identifier
doi:10.1214/EJP.v20-4251

Mathematical Reviews number (MathSciNet)
MR3425537

Zentralblatt MATH identifier
1328.60212

Rights