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On approximate pattern matching for a class of Gibbs random fields

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Jean-Rene Chazottes, Frank Redig, Evgeny Verbitskiy

Probability · Submitted 1 Mar 2005

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

The authors' main claim We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$.

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arXiv IDmath/0503008 (version 3)
Pith IDNFXIUM3O, Pith's permanent record of this paper and its review
CitationEvgeny Verbitskiy, Frank Redig, Jean-Rene Chazottes. "On approximate pattern matching for a class of Gibbs random fields." arXiv:math/0503008 (2005). https://pith.science/paper/NFXIUM3O
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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, 2,276 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.64 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.

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 prove an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. result 0.82 0.95 0.87 asserted 1.00
s1 From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns. result 0.92 0.95 0.18 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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  • references and citing sentences
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  • P abstract
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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 an exponential approximation for the law of approximate occurrence of typical patterns for a class of Gibssian sources on the lattice $\mathbb{Z}^d$, $d\ge2$. From this result, we deduce a law of large numbers and a large deviation result for the waiting time of distorted patterns.

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