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Large Deviation Principle for the Exploration Process of the Configuration Model

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Shankar Bhamidi, Amarjit Budhiraja, Paul Dupuis, Ruoyu Wu

Probability · Submitted 6 Aug 2017

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

The authors' main claim We establish a large deviation principle for the exploration process associated with the configuration model.

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arXiv ID1708.01832 (version 2)
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CitationAmarjit Budhiraja, Paul Dupuis, Ruoyu Wu, Shankar Bhamidi. "Large Deviation Principle for the Exploration Process of the Configuration Model." arXiv:1708.01832 (2017). https://pith.science/paper/RS3AFNUV
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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.02 · states quantitative result 0.10 · compares with prior results 0.05 · mentions code or data availability 0.02.

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

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be obtained from an infinite dimensional Markov chain referred to as the exploration process. We establish a large deviation principle for the exploration process associated with the configuration model. Proofs rely on a representation of the exploration process as a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Applications of the large deviation results, for studying asymptotic behavior of the degree sequence in large components of the random graphs, are discussed.

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 configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. background 1.00 0.06 0.02 asserted 1.00
s1 The component structure of such random graphs can be obtained from an infinite dimensional Markov chain referred to as the exploration process. background 0.96 0.09 0.03 asserted 1.00
s2 We establish a large deviation principle for the exploration process associated with the configuration model. contribution 0.85 0.97 0.91 asserted 1.00
s3 Proofs rely on a representation of the exploration process as a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. method 1.00 0.84 0.05 asserted 1.00
s4 Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. method 0.99 0.58 0.03 asserted 1.00
s5 Applications of the large deviation results, for studying asymptotic behavior of the degree sequence in large components of the random graphs, are discussed. contribution 0.57 0.78 0.06 asserted 0.88

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

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be obtained from an infinite dimensional Markov chain referred to as the exploration process. We establish a large deviation principle for the exploration process associated with the configuration model. Proofs rely on a representation of the exploration process as a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Applications of the large deviation results, for studying asymptotic behavior of the degree sequence in large components of the random graphs, are discussed.

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