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 $gamma to p
i/4.$ 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.
The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors.
