Random wavefunctions and percolation

Abstract

Recently it was conjectured that nodal domains of random wavefunctions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wavefunction correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wavefunctions belong to the same universality class as non-correlated critical percolation. Second, we argue that level domains of random wavefunctions are described by the non-critical percolation model.