Counting nodal domains

Georg Foltin

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arXiv · nlin/0302049

Counting nodal domains

Georg Foltin

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Abstract

We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical approach could be helpful to decide whether the pattern of nodal domains belongs to the universality class of short-ranged percolation. This is not completely evident since we find (weak) long-ranged correlations between distant avoided nodal intersections.

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Georg Foltin. 2003-02-20. Counting nodal domains. https://arxiv.org/abs/nlin/0302049

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