Shadow and percolation II: discrete and continuous landscapes with correlations

Abstract

In this paper we consider a discrete or continuous landscape with correlations and we consider a source of light (a sun) at infinity emitting parallel rays of light making a slope l with the horizontal plane. Depending on the value of l some portions of the landscape may be lit by the sun or be in the shadow. Under some assumptions, we show that if l is big enough then there exists a giant component of light. However, if l>0 is small enough and if we are in discrete case, then there exists a giant component of shadow. We relate this problem to the study of the percolation properties of a new random planar field.