Almost all eigenfunctions of a rational polygon are uniformly distributed

Jens Marklof, Zeév Rudnick

Type: Article

Publication Date: 2012-01-17

Citations: 36

DOI: https://doi.org/10.4171/jst/23

Abstract

We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.

Locations

Journal of Spectral Theory - View - PDF
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Almost all eigenfunctions of a rational polygon are uniformly distributed	2011	Jens Marklof Zeév Rudnick
+	Almost all eigenfunctions of a rational polygon are uniformly distributed	2011	Jens Marklof Zeév Rudnick
+	Dirichlet series of functions, regular in convex polygons	1980	Yu. I. Mel'nik
+	Asymptotic behavior of the dirichlet kernel of fourier sums with respect to a polygon	1988	A. Podkorytov
+ PDF Chat	Spectrum of the Laplacian on regular polyhedra	2020	Evan Greif Daniel T. Kaplan Robert S. Strichartz Samuel C. Wiese
+	Asymptotics for orthonormal rational functions on the interval	2011	Karl Deckers
+	Delocalisation of eigenfunctions on large genus random surfaces	2020	Joe Thomas
+	Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution	2013	Junehyuk Jung Steve Zelditch
+	Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution	2013	Junehyuk Jung Steve Zelditch
+	Counting nodal components of boundary-adapted arithmetic random waves	2019	James Cann
+	Spectrum of the Laplacian on Regular Polyhedra	2018	Evan Greif Daniel M. Kaplan Robert S. Strichartz Samuel C. Wiese
+	Spectrum of the Laplacian on Regular Polyhedra	2018	Evan Greif Daniel T. Kaplan Robert S. Strichartz Samuel C. Wiese
+	Representation of regular functions by Dirichlet series in closed convex polygons	1978	Yu. I. Mel'nik
+	A Remainder Estimate for The Asymptotic Law for The Distribution of Elgenvalues of The Laplacian in a PolyGonal Domain	1982	Fumioki Asakura
+	Nodal length fluctuations for arithmetic random waves	2011	Manjunath Krishnapur Pär Kurlberg Igor Wigman
+	Expansions of functions into Dirichlet series on closed convex polygons	1979	А. М. Седлетский
+	Nodal length fluctuations for arithmetic random waves	2011	Manjunath Krishnapur Pär Kurlberg Igor Wigman
+	Points on nodal lines with given direction.	2018	Zeév Rudnick Igor Wigman
+	Efficiency and localisation for the first Dirichlet eigenfunction	2019	M. van den Berg Francesco Della Pietra Giuseppina di Blasio Nunzia Gavitone
+	Efficiency and localisation for the first Dirichlet eigenfunction	2019	M. van den Berg Francesco Della Pietra Giuseppina di Blasio Nunzia Gavitone

Works That Cite This (35)

Action	Title	Year	Authors
+ PDF Chat	Concentration and non-concentration of eigenfunctions of second-order elliptic operators in layered media	2024	Assia Benabdallah Matania Ben–Artzi Yves Dermenjian
+	Equidistribution of toral eigenfunctions along hypersurfaces	2018	Hamid Hezari Gabriel Rivière
+ PDF Chat	Superscarred quasimodes on flat surfaces with conical singularities	2022	Omer Friedland Henrik Ueberschär
+ PDF Chat	Around quantum ergodicity	2021	Semyon Dyatlov
+ PDF Chat	Remarks on quantum ergodicity	2013	Gabriel Rivière
+ PDF Chat	An algorithm for identifying eigenvectors exhibiting strong spatial localization	2022	Jeffrey S. Ovall Robyn Reid
+	L norms, nodal sets, and quantum ergodicity	2016	Hamid Hezari Gabriel Rivière
+ PDF Chat	Energy distribution for Dirichlet eigenfunctions on right triangles	2024	Hans Christianson Daniel Pezzi
+	$L^p$ norms, nodal sets, and quantum ergodicity	2014	Hamid Hezari Gabriel Rivière
+ PDF Chat	Small Scale Equidistribution of Eigenfunctions on the Torus	2016	Stephen Lester Zeév Rudnick

Works Cited by This (10)

Action	Title	Year	Authors
+ PDF Chat	Nearest-neighbor distribution for singular billiards	2002	E. Bogomolny Olivier Giraud C. Schmit
+ PDF Chat	Ergodic billiards that are not quantum unique ergodic	2010	Andrew Hassell
+	Ergodicity of Billiard Flows and Quadratic Differentials	1986	Steven P. Kerckhoff Howard Masur John Smillie
+	State scarring by ‘‘ghosts’’ of periodic orbits	1994	Paolo Bellomo T. Uzer
+ PDF Chat	Ergodicity of eigenfunctions for ergodic billiards	1996	Steven Zelditch Maciej Zworski
+ PDF Chat	Quantum Limits on Flat Tori	1997	Dmitry Jakobson
+ PDF Chat	Quantum ergodicity ofC * dynamical systems	1996	Steven Zelditch
+ PDF Chat	First Experimental Observation of Superscars in a Pseudointegrable Barrier Billiard	2006	E. Bogomolny Barbara Dietz Thomas Friedrich M. Miski-Oglu A. Richter F. Schäfer C. Schmit
+ PDF Chat	Eigenfunction Concentration for Polygonal Billiards	2009	Andrew Hassell Luc Hillairet Jeremy L. Marzuola
+ PDF Chat	Statistics of Wave Functions for a Point Scatterer on the Torus	2012	Zeév Rudnick Henrik Ueberschär