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Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Tianshi Lu, Chunsheng Ma, Yimin Xiao

Probability · Submitted 30 Dec 2021

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

The authors' main claim In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.

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arXiv ID2112.14874 (version 1)
Pith IDPMD5DA6L, Pith's permanent record of this paper and its review
CitationChunsheng Ma, Tianshi Lu, Yimin Xiao. "Strong Local Nondeterminism and Exact Modulus of Continuity for Isotropic Gaussian Random Fields on Compact Two-Point Homogeneous Spaces." arXiv:2112.14874 (2021). https://pith.science/paper/PMD5DA6L
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,318 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 0.01 · states quantitative result 0.22 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. background 0.83 0.26 0.04 asserted 0.79
s1 In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths. contribution 0.79 0.96 0.88 asserted 1.00

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

What was examined, and what was not

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  • C citations
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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

This paper is concerned with sample path properties of isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field based on the high-frequency behavior of its angular power spectrum, and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.

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