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An ergodic theorem for Delone dynamical systems and existence of the integrated density of states

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Daniel Lenz, Peter Stollmann

Mathematical Physics · Submitted 10 Oct 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As an application, we prove existence of the integrated density of states in the sense of uniform convergence in distribution for the associated random operators.

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arXiv IDmath-ph/0310017 (version 1)
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CitationDaniel Lenz, Peter Stollmann. "An ergodic theorem for Delone dynamical systems and existence of the integrated density of states." arXiv:math-ph/0310017 (2003). https://pith.science/paper/O6THLLYS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,270 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.02 · states quantitative result 0.05 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we prove existence of the integrated density of states in the sense of uniform convergence in distribution for the associated random operators.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. contribution 0.82 0.96 0.37 asserted 1.00
s1 As an application, we prove existence of the integrated density of states in the sense of uniform convergence in distribution for the associated random operators. result 0.96 0.95 0.52 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we prove existence of the integrated density of states in the sense of uniform convergence in distribution for the associated random operators.

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