Fixed frequency eigenfunction immersions and supremum norms of random waves

Boris Hanin, Yaiza Canzani

Type: Article

Publication Date: 2015-09-01

Citations: 14

DOI: https://doi.org/10.3934/era.2015.22.76

Abstract

A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and others on upper bounds for the sup-norms of random linear combinations of high frequency eigenfunctions.

Locations

Electronic Research Announcements - View - PDF
arXiv (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	Mean of the $L^\infty$-norm for $L^2$-normalized random waves on compact aperiodic Riemannian manifolds	2013	Yaiza Canzani Boris Hanin
+	Mean of the $L^\infty$-norm for $L^2$-normalized random waves on compact aperiodic Riemannian manifolds	2013	Yaiza Canzani Boris Hanin
+	A sharp Wasserstein uncertainty principle for Laplace eigenfunctions	2021	Mayukh Mukherjee
+	Restriction of Laplace-Beltrami eigenfunctions to arbitrary sets on manifolds	2019	Suresh Eswarathasan Malabika Pramanik
+	Restriction of Laplace-Beltrami eigenfunctions to arbitrary sets on manifolds	2019	Suresh Eswarathasan Malabika Pramanik
+	On the Restriction of Laplace–Beltrami Eigenfunctions and Cantor-Type Sets	2021	Suresh Eswarathasan Malabika Pramanik
+ PDF Chat	Critical radii and suprema of random waves over Riemannian manifolds	2025	Renjie Feng Dong Yao Robert J. Adler
+ PDF Chat	Concentration et randomisation universelle de sous-espaces propres	2017	Rafik Imekraz
+	Restriction of Laplace-Beltrami eigenfunctions to Cantor-type sets on manifolds	2019	Suresh Eswarathasan Malabika Pramanik
+	Isoperimetric bounds for Wentzel-Laplace eigenvalues on Riemannian manifolds	2020	Aïssatou M. Ndiaye
+	Isoperimetric bounds for Wentzel-Laplace eigenvalues on Riemannian manifolds.	2020	Aïssatou M. Ndiaye
+ PDF Chat	Growth of high Lp norms for eigenfunctions : an application of geodesic beams	2023	Yaiza Canzani Jeffrey Galkowski
+	Eigenfunctions and a lower bound on the Wasserstein distance	2021	Nicolò De Ponti Sara Farinelli
+ PDF Chat	None	1976	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1970	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1930	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1979	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1937	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1905	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag
+ PDF Chat	None	1994	Joachim Cuntz David Masser Tobias Colding Daniel Huybrechts Jun-Muk Hwang Olivier Schiffmann Jakob Stix Gábor Székelyhidi Franz Stückle Druck Und Verlag

Works That Cite This (13)

Action	Title	Year	Authors
+ PDF Chat	Volume distribution of nodal domains of random band-limited functions	2017	Dmitry Beliaev Igor Wigman
+ PDF Chat	Effective bounds for monochromatic connectivity measures in two dimensions	2021	Matthew de Courcy-Ireland Suresh Eswarathasan
+ PDF Chat	Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds	2020	Matthew de Courcy-Ireland
+ PDF Chat	Expected Values of Eigenfunction Periods	2015	Suresh Eswarathasan
+	A Quantitative Central Limit Theorem for the Euler-Poincar\'e Characteristic of Random Spherical Eigenfunctions	2016	Valentina Cammarota Domenico Marinucci
+ PDF Chat	A quantitative central limit theorem for the Euler–Poincaré characteristic of random spherical eigenfunctions	2018	Valentina Cammarota Domenico Marinucci
+ PDF Chat	A necessary and sufficient condition for probabilistic continuity on a boundaryless compact Riemannian manifold	2022	Rafik Imekraz
+	Volume distribution of nodal domains of random band-limited functions	2016	Dmitry Beliaev Igor Wigman
+	Shrinking scale equidistribution for monochromatic random waves on compact manifolds.	2019	Matthew de Courcy-Ireland
+	Small-scale equidistribution for random spherical harmonics	2017	Matthew de Courcy-Ireland

Works Cited by This (19)

Action	Title	Year	Authors
+	Random Fields and Geometry	2007	Robert J. Adler Jonathan Taylor
+ PDF Chat	A kernel-based classifier on a Riemannian manifold	2008	Jean-Michel Loubès Bruno Pelletier
+ PDF Chat	$L^p$ properties for Gaussian random series	2008	Antoine Ayache Nikolay Tzvetkov
+ PDF Chat	The spectral function of an elliptic operator	1968	Lars Hörmander
+	Fine Structure of Zoll Spectra	1997	Steve Zelditch
+	On a set of polarized Kähler metrics on algebraic manifolds	1990	Gang Tian
+	On the spectrum of positive elliptic operators and periodic bicharacteristics	1975	J. J. Duistermaat Victor Guillemin
+	Median and mean of the Supremum of $L^2$ normalized random holmorphic fields	2013	Renjie Feng Steve Zelditch
+ PDF Chat	Nodal length fluctuations for arithmetic random waves	2013	Manjunath Krishnapur Pär Kurlberg Igor Wigman
+ PDF Chat	The Leray measure of nodal sets for random eigenfunctions on the torus	2008	Ferenc Oravecz Zeév Rudnick Igor Wigman