On the Bogomolny-Schmit conjecture

D. Beliaev, Z. Kereta

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Article number455003
JournalJournal of Physics A: Mathematical and Theoretical
Issue number45
Publication statusPublished - 15 Nov 2013
Externally publishedYes


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