# Applications of small scale quantum ergodicity in nodal sets

@article{Hezari2016ApplicationsOS,
title={Applications of small scale quantum ergodicity in nodal sets},
author={Hamid Hezari},
journal={arXiv: Analysis of PDEs},
year={2016}
}
• Hamid Hezari
• Published 7 June 2016
• Mathematics
• arXiv: Analysis of PDEs
The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinking radius $r(\lambda) \to 0$, then one can achieve improvements on the recent upper bounds of Logunov and Logunov-Malinnikova on the size of nodal sets, according to a certain power of $r(\lambda)$. We also show that the order of vanishing results of Donnelly-Fefferman and Dong can be improved. Since by the results of…
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DOI: https://doi.org/10.1090/noti1958 thor [Z17, Z18]. One of the leaders in the field, Nalini Anantharaman, has just given a plenary address on quantum chaos at the 2018 ICM, and interested readers
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