Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds

Felix Knöppel

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arXiv · 2312.01493

Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds

Felix Knöppel

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Abstract

This paper is concerned with zero currents of random section of a Hermitian line bundle $E$ over a compact oriented Riemannian manifold. Given a metric connection, heat flow yields a natural 1-parameter family of probability measures on the space of smooth sections $\Gamma E$. It is shown that the corresponding family of random zero currents connects the curvature of the bundle to the ground state zero current.

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Felix Knöppel. 2023-12-03. Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds. https://arxiv.org/abs/2312.01493

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