Abstract
Let ( M , g ) (\mathcal {M},g) be a smooth compact Riemannian surface with no boundary. Given a smooth vector field V V with finitely many zeros on M \mathcal {M} , we study the distribution of the number of tangencies to V V of the nodal components of random band-limited functions. It is determined that in the high-energy limit, these obey a universal deterministic law, independent of the surface M \mathcal {M} and the vector field V V , that is supported precisely on the even integers 2 Z > 0 2 \mathbb {Z}_{> 0} .
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