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Coarse-graining schemes for stochastic lattice systems with short and long-range interactions.

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M. A. Katsoulakis, P.Plechac, L. Rey-Bellet, D. K. Tsagkarogiannis

Numerical Analysis · Submitted 7 Mar 2010

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

The authors' main claim We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.

how it is stated · asserted 1.00 read the record →

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arXiv ID1003.1506 (version 1)
Pith IDCP6LFV3V, Pith's permanent record of this paper and its review
CitationD. K. Tsagkarogiannis, L. Rey-Bellet, M. A. Katsoulakis, P.Plechac. "Coarse-graining schemes for stochastic lattice systems with short and long-range interactions.." arXiv:1003.1506 (2010). https://pith.science/paper/CP6LFV3V
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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, 3,572 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.

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 develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. contribution 1.00 0.95 0.08 asserted 1.00
s1 We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. method 0.59 0.93 0.09 asserted 0.96
s2 We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. contribution 0.71 0.95 0.19 asserted 1.00
s3 We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions. contribution 0.52 0.95 0.24 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.97 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.

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