The Weyl-Heisenberg ensemble: Statistical mechanics meets time-frequency analysis

Luís Daniel Abreu, João Pereira, Jose Luis Romero, Salvatore Torquato

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present our recent work on the Weyl-Heisenberg ensemble and its statistical properties [4]. The WH ensemble is a class of determinantal point processes associated with the Schrödinger representation of the Heisenberg group. As a special example, WH ensembles include a multi-layer extension of the Ginibre ensemble modeling the distribution of electrons in higher Landau levels. We describe the hyperuniformity of WH ensembles, which characterizes a state of matter for which (scaled) density fluctuations diminish towards zero at the largest length scales. Our approach is based on methods from time-frequency analysis. We introduce the main results from [4] highlighting time-frequency techniques and connections to the theory of polyanalytic functions, and also present some small extensions.

Original languageEnglish (US)
Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
EditorsGholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages199-202
Number of pages4
ISBN (Electronic)9781538615652
DOIs
StatePublished - Sep 1 2017
Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
Duration: Jul 3 2017Jul 7 2017

Publication series

Name2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Other

Other12th International Conference on Sampling Theory and Applications, SampTA 2017
CountryEstonia
CityTallinn
Period7/3/177/7/17

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Statistics, Probability and Uncertainty
  • Analysis
  • Statistics and Probability
  • Applied Mathematics

Keywords

  • Weyl-Heisenberg ensemble
  • disorder
  • fluctuations
  • higher Landau levels
  • hyperuniformity

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