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Quantitative stochastic homogenization of the G equation

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William Cooperman

Analysis of PDEs · Submitted 9 Nov 2021

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

The authors' main claim We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence.

how it is stated · asserted 1.00 read the record →

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arXiv ID2111.05221 (version 2)
Pith IDOAIHRVPL, Pith's permanent record of this paper and its review
CitationWilliam Cooperman. "Quantitative stochastic homogenization of the G equation." arXiv:2111.05221 (2021). https://pith.science/paper/OAIHRVPL
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,278 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.59 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.31 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet and Souganidis, who proved qualitative homogenization in a more general ergodic environment.

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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 prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. result 0.58 0.96 0.94 asserted 1.00
s1 Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet and Souganidis, who proved qualitative homogenization in a more general ergodic environment. method 0.99 0.63 0.06 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 prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet and Souganidis, who proved qualitative homogenization in a more general ergodic environment.

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1 arXiv paper cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • As in the previous section, the proofs are nearly identical to those in [ref] , with a bit of care taken to keep track of the dependence of the constants on $V$.

    On the random G equation with nonzero divergence · Random fluctuations in first-passage time · 0.81

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