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Let $(M,g)$ be a smooth compact Riemannian surface with no boundary. Given a smooth vector field $V$ with finitely many zeroes on $M$, we study the distribution of the number… Click to show full abstract
Let $(M,g)$ be a smooth compact Riemannian surface with no boundary. Given a smooth vector field $V$ with finitely many zeroes on $M$, we study the distribution of the number of tangencies to $V$ 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 $M$ and the vector field $V$, that is supported precisely on the even integers $2 \mathbb{Z}_{> 0}$.
Keywords:
random band;
band limited;
nodal components;
limited functions;
components random;
distribution
Journal Title: Transactions of the American Mathematical Society
Year Published: 2020
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Journal Title: Transactions of the American Mathematical Society
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!