Asymptotics for Lipschitz percolation above tilted planes

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 $dto infty$ 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.