On a CLT for Gibbs fields and its functional version.

DOI10.1016/S0167-7152(03)00177-9zbMath1113.60304OpenAlexW2061840259MaRDI QIDQ1423130

Alberto L. Maltz, Jorge D. Samur

Publication date: 14 February 2004

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(03)00177-9

zbMATH Keywords

Gibbs measureUniform central limit theoremContinuous Wiener processNonuniform \(\varphi\)-mixingPartial-sums processRandom fields on integer lattice

Mathematics Subject Classification ID

Random fields (60G60) Central limit and other weak theorems (60F05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Functional limit theorems; invariance principles (60F17)

Cites Work

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• Characterisations of set-indexed Brownian motion and associated conditions for finite-dimensional convergence
• Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes
• An almost sure invariance principle for partial sums associated with a random field
• Decay of correlations under Dobrushin's uniqueness condition and its applications
• On the central limit theorem for stationary mixing random fields
• A uniform central limit theorem for nonuniform \(\phi\)-mixing random fields
• Gibbs measures and phase transitions
• On the central limit theorem for nonuniform \(\varphi\)-mixing random fields
• A central limit theorem for nonuniform \(\varphi\)-mixing random fields with infinite variance

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