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arXiv · 2003.03165

An enhanced uncertainty principle for the Vaserstein distance

Tom Carroll·Xavier Massaneda·Joaquim Ortega-Cerdà
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Abstract

We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function $f$ with mean zero, either the size of the zero set of the function or the cost of transporting the mass of the positive part of $f$ to its negative part must be big. We also provide a sharp upper estimate of the transport cost of the positive part of an eigenfunction of the Laplacian. This proves a conjecture of Steinerberger and provides a lower bound of the size of the nodal set of the eigenfunction.

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Tom Carroll, Xavier Massaneda, Joaquim Ortega-Cerdà. 2020-03-06. An enhanced uncertainty principle for the Vaserstein distance. https://doi.org/10.1112/blms.12390

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