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Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities

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François Bolley (LPMA), Ivan Gentil (ICJ), Arnaud Guillin (LMBP)

Probability · Submitted 4 Jul 2015

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

The authors' main claim They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations.

how it is stated · asserted 1.00 read the record →

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arXiv ID1507.01086 (version 4)
Pith IDMDRDRV5I, Pith's permanent record of this paper and its review
CitationArnaud Guillin (LMBP), Fran\c{c}ois Bolley (LPMA), Ivan Gentil (ICJ). "Dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities." arXiv:1507.01086 (2015). https://pith.science/paper/MDRDRV5I
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,124 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.25 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations.

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 In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. contribution 0.90 0.65 0.13 asserted 0.67
s1 For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. method 1.00 0.77 0.04 asserted 1.00
s2 These refinements can be written as a deficit in the classical inequalities. result 0.61 0.78 0.17 asserted 0.97
s3 They have the right scale with respect to the dimension. result 0.79 0.78 0.09 asserted 1.00
s4 They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations. interpretation 0.73 0.81 0.55 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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not examined
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  • references and citing sentences
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  • P abstract
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  • T body sentences
  • 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

In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a deficit in the classical inequalities. They have the right scale with respect to the dimension. They lead to sharpened concentration properties as well as refined contraction bounds, convergence to equilibrium and short time behaviour for the laws of solutions to stochastic differential equations.

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