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From interacting particle systems to random matrices

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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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Patrik L. Ferrari (Bonn University)

Mathematical Physics · Submitted 28 Aug 2010

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

The authors' main claim Therefore the connections between growth models and random matrices is only partial.

how it is stated · asserted 1.00 read the record →

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arXiv ID1008.4853 (version 3)
Pith IDAPODGX4Z, Pith's permanent record of this paper and its review
CitationPatrik L. Ferrari (Bonn University). "From interacting particle systems to random matrices." arXiv:1008.4853 (2010). https://pith.science/paper/APODGX4Z
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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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,792 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.02 · states quantitative result 0.08 · compares with prior results 0.60 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.

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 contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. contribution 0.78 0.42 0.04 asserted 0.80
s1 We discuss the large time distribution and processes and their dependence on the class on initial condition. contribution 0.99 0.55 0.07 asserted 0.67
s2 This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. interpretation 0.89 0.27 0.51 asserted 1.00
s3 Some of the fluctuation laws were first discovered in random matrix models. background 1.00 0.05 0.04 asserted 0.98
s4 Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. result 0.61 0.29 0.11 asserted 1.00
s5 Therefore the connections between growth models and random matrices is only partial. interpretation 0.79 0.29 0.53 asserted 1.00

What kind of paper the classifier reports this is: review 0.76 · evidence from literature 0.53.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.

Human review

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How the literature uses it

5 arXiv papers cite this in 7 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

Papers citing it · 1 sentence without a confident label

Compares with it 1 paper
Cites it as background 4 papers

What it cites · 9 sentences without a confident label

Cites as background 1 paper
  • More information about these processes like properties and references can be found for example in the reviews [ref] .

    Random Growth Models · Definition of the limit processes · 1.00

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