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Berry-Esseen bound for the Brownian motions on hyperbolic 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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Yuichi Shiozawa

Probability · Submitted 8 Sep 2023

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

The authors' main claim We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space.

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arXiv ID2309.04325 (version 1)
Pith IDQM4V6G22, Pith's permanent record of this paper and its review
CitationYuichi Shiozawa. "Berry-Esseen bound for the Brownian motions on hyperbolic spaces." arXiv:2309.04325 (2023). https://pith.science/paper/QM4V6G22
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The compiled record

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, 2,885 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.42 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our approach is based on the repetitive use of the Millson formula and the integration by parts formula.

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 We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. result 0.82 0.96 0.88 asserted 1.00
s1 We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. result 0.91 0.92 0.18 asserted 1.00
s2 Our approach is based on the repetitive use of the Millson formula and the integration by parts formula. method 1.00 0.83 0.03 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

We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our approach is based on the repetitive use of the Millson formula and the integration by parts formula.

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