Traces of Random Operators Associated with Self-Affine Delone Sets and Shubin’s Formula

Scott Edward Schmieding, Rodrigo Treviño*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We study operators defined on a Hilbert space defined by a self-affine Delone set Λ and show that the usual trace of a restriction of the operator to finite-dimensional subspaces satisfies a certain lim sup law controlled by traces on a certain subalgebra. The asymptotic traces are defined through asymptotic cycles, or Rd-invariant distributions of a dynamical system defined by Λ. We use this to refine Shubin’s trace formula for certain self-adjoint operators acting on ℓ2(Λ) and show that the errors of convergence in Shubin’s formula are given by these traces.

Original languageEnglish (US)
Pages (from-to)2575-2597
Number of pages23
JournalAnnales Henri Poincare
Volume19
Issue number9
DOIs
StatePublished - Sep 1 2018

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Random Operators
Self-affine
Trace
operators
Hilbert space
dynamical systems
Invariant Distribution
Trace Formula
constrictions
Operator
Self-adjoint Operator
Subalgebra
cycles
Dynamical system
Subspace
Restriction
Cycle

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

Cite this

Schmieding, Scott Edward ; Treviño, Rodrigo. / Traces of Random Operators Associated with Self-Affine Delone Sets and Shubin’s Formula. In: Annales Henri Poincare. 2018 ; Vol. 19, No. 9. pp. 2575-2597.
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Traces of Random Operators Associated with Self-Affine Delone Sets and Shubin’s Formula. / Schmieding, Scott Edward; Treviño, Rodrigo.

In: Annales Henri Poincare, Vol. 19, No. 9, 01.09.2018, p. 2575-2597.

Research output: Contribution to journalArticle

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