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Generalized $\Gamma$ calculus and application to interacting particles on a graph

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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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Pierre Monmarché

Probability · Submitted 20 Oct 2015

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

The authors' main claim The classical Bakry-\'Emery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as hypoellipticity, hypocoercivity, functional inequalities or Wasserstein contraction.

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arXiv ID1510.05936 (version 4)
Pith IDPSR6QIOZ, Pith's permanent record of this paper and its review
CitationPierre Monmarch\'e. "Generalized $\Gamma$ calculus and application to interacting particles on a graph." arXiv:1510.05936 (2015). https://pith.science/paper/PSR6QIOZ
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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, 3,093 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.30 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

The classical Bakry-\'Emery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as hypoellipticity, hypocoercivity, functional inequalities or Wasserstein contraction. In particular we obtain the optimal speed of convergence to equilibrium for any ergodic Ornstein-Uhlenbeck process, which is given by the spectral gap of the drift matrix and the size of the corresponding Jordan blocks. We also study chains of $N$ interacting overdamped particles and establish for their invariant measures log-Sobolev inequalities with constants of order $N^2$, which is optimal.

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 The classical Bakry-\'Emery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as hypoellipticity, hypocoercivity, functional inequalities or Wasserstein contraction. contribution 0.96 0.77 0.21 asserted 1.00
s1 In particular we obtain the optimal speed of convergence to equilibrium for any ergodic Ornstein-Uhlenbeck process, which is given by the spectral gap of the drift matrix and the size of the corresponding Jordan blocks. result 0.99 0.93 0.23 asserted 1.00
s2 We also study chains of $N$ interacting overdamped particles and establish for their invariant measures log-Sobolev inequalities with constants of order $N^2$, which is optimal. result 0.86 0.95 0.29 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.68 · evidence from proof or derivation 1.00.

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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

The classical Bakry-\'Emery calculus is extended to study, for degenerated (non-elliptic, non-reversible, or non-diffusive) Markov processes, questions such as hypoellipticity, hypocoercivity, functional inequalities or Wasserstein contraction. In particular we obtain the optimal speed of convergence to equilibrium for any ergodic Ornstein-Uhlenbeck process, which is given by the spectral gap of the drift matrix and the size of the corresponding Jordan blocks. We also study chains of $N$ interacting overdamped particles and establish for their invariant measures log-Sobolev inequalities with constants of order $N^2$, which is optimal.

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5 arXiv papers cite this in 9 sentences

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