Random wave functions and percolation

Abstract

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

13 pages

References in corpus (6)

• Nodal domains statistics - a criterion for quantum chaos
• Percolation model for nodal domains of chaotic wave functions
• Universality of finite-size corrections to the number of critical percolation clusters
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• Geometry and scaling of tangled vortex lines in three-dimensional random wave fields
• Nodal domains of a non-separable problem - the right angled isosceles triangle
• Fluctuations of the number of excursion sets of planar Gaussian fields
• Gaussian Waves on the Regular Tree
• On Bogomolny-Schmit conjecture
• Percolation without FKG
• Eigenfunctions and Nodal Sets
• Nodal domains of Maass forms II
• Topological effects and conformal invariance in long-range correlated random surfaces
• Percolation of strongly correlated Gaussian fields I. Decay of subcritical connection probabilities
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• Vortex reconnection rate, and loop birth rate, for a random wavefield
• Short and Long Range Screening of Optical Singularities
• Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics
• On the Nodal Count Statistics for Separable Systems in any Dimension
• On Pleijel's nodal domain theorem
• On toral eigenfunctions and the random wave model
• Anomalies in local Weyl laws and applications to random topology at critical dimension
• Local Extrema in Quantum Chaos
• Level sets percolation on chaotic graphs