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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.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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