On Bogomolny-Schmit conjecture

Abstract

Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer experiments showed that the mean number of clusters per vertex and the mean number of nodal domains per unit area are very close but different. Since the original argument was mostly supported by numerics, it was believed that the percolation model is wrong. In this paper we give some numerical evidence in favour of the percolation model.

6 pages, 2 figures. To be published in Journal of Physics A: Mathematical and Theoretical

References in corpus (2)

• Random wave functions and percolation
• On the distribution of the nodal sets of random spherical harmonics

Cited by in corpus (8)

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• On the distribution of the critical values of random spherical harmonics
• Discretisation schemes for level sets of planar Gaussian fields
• Nodal Statistics On Quantum Graphs
• On the number of excursion sets of planar Gaussian fields
• Universality of nodal count distribution in large metric graphs
• Effective bounds for monochromatic connectivity measures in two dimensions
• Three central limit theorems for the unbounded excursion component of a Gaussian field