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Asymptotic number of connected components of nodal sets of random functions

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If you have a question about this talk, please contact Jan Bohr.

Abstract. Consider a random smooth (Gaussian) field and associate to it its (zero level) nodal set i.e. all points that map to zero. Many questions can be asked about these nodal sets: total surface measure, number of connected components, percolative properties, etc. The focus of the talk will be to address the second question and explain Nazarov and Sodin’s proof (2016) of a corresponding law of large numbers. I will also (briefly) link the random theory to the deterministic problem of understanding the nodal sets associated to the eigenfunctions of the Laplace operator.

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