Quantitative equidistribution and the local statistics of the spectrum of a flat torus

Elon Lindenstrauss; Amir Mohammadi; Zhiren Wang

doi:10.1007/s11854-023-0332-x

Quantitative equidistribution and the local statistics of the spectrum of a flat torus

Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.

Original language	English (US)
Pages (from-to)	181-234
Number of pages	54
Journal	Journal d'Analyse Mathematique
Volume	151
Issue number	1
DOIs	https://doi.org/10.1007/s11854-023-0332-x
State	Published - Dec 2023

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics

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title = "Quantitative equidistribution and the local statistics of the spectrum of a flat torus",

abstract = "We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.",

author = "Elon Lindenstrauss and Amir Mohammadi and Zhiren Wang",

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AU - Wang, Zhiren

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N2 - We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.

AB - We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.

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Quantitative equidistribution and the local statistics of the spectrum of a flat torus

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