The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its Regularity

Abstract

Next article The Description of a Random Field by Means of Conditional Probabilities and Conditions of Its RegularityP. L. DobruschinP. L. Dobruschinhttps://doi.org/10.1137/1113026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , Yu. V. Linnik, Independent and Stationarily Connected Variables, Izd-vo "Nauka", Moscow, 1965, (In Russian.) Google Scholar[2] B. Rjauba, The central limit theorem for sums of series of weakly dependent random variables, Litovsk. Mat. Sb., 2 (1962), 193–205, (In Russian.) MR0169274 (29:6526) 0129.31201 Google Scholar[3] Yu. A. Rozanov, On Gaussian random fields with given conditional distributions, Theory Prob. Applications, 12 (1967), 381–391 10.1137/1112050 0212.20101 LinkGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails A Functional Central Limit Theorem for Polaron Path MeasuresCommunications on Pure and Applied Mathematics, Vol. 9 | 12 August 2022 Cross Ref Description of random fields by systems of conditional distributionsArmenian Journal of Mathematics | 3 June 2022 Cross Ref Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equationThe Annals of Applied Probability, Vol. 32, No. 3 | 1 Jun 2022 Cross Ref An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactionsJournal of Applied Probability, Vol. 59, No. 2 | 30 March 2022 Cross Ref Decimations for two-dimensional Ising and rotator modelsJournal of Mathematical Physics, Vol. 63, No. 3 | 1 Mar 2022 Cross Ref Stem and topological entropy on Cayley treesMathematical Physics, Analysis and Geometry, Vol. 25, No. 1 | 22 December 2021 Cross Ref Twelve tales in mathematical physics: An expanded Heineman prize lectureJournal of Mathematical Physics, Vol. 63, No. 2 | 1 Feb 2022 Cross Ref Finitary codings for the random-cluster model and other infinite-range monotone modelsElectronic Journal of Probability, Vol. 27, No. none | 1 Jan 2022 Cross Ref Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteriaJournal of Mathematical Physics, Vol. 62, No. 10 | 1 Oct 2021 Cross Ref Combinatorial Approach to the Description of Random FieldsLobachevskii Journal of Mathematics, Vol. 42, No. 10 | 19 October 2021 Cross Ref When Janson meets McDiarmid: Bounded difference inequalities under graph-dependenceStatistics & Probability Letters, Vol. 17 | 1 Oct 2021 Cross Ref A spectral condition for spectral gap: fast mixing in high-temperature Ising modelsProbability Theory and Related Fields, Vol. 276 | 20 August 2021 Cross Ref Refinement of quantum Markov states on treesJournal of Statistical Mechanics: Theory and Experiment, Vol. 2021, No. 8 | 20 August 2021 Cross Ref Infinite DLR measures and volume-type phase transitions on countable Markov shiftsNonlinearity, Vol. 34, No. 7 | 23 June 2021 Cross Ref On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systemsJournal of Mathematical Physics, Vol. 62, No. 6 | 1 Jun 2021 Cross Ref Random Fields in Physics, Biology and Data ScienceFrontiers in Physics, Vol. 9 | 15 April 2021 Cross Ref Gibbsian Representations of Continuous Specifications: The Theorems of Kozlov and Sullivan RevisitedCommunications in Mathematical Physics, Vol. 382, No. 2 | 11 February 2021 Cross Ref Uniqueness of the Gibbs state of the BEG model in the disordered region of parametersLetters in Mathematical Physics, Vol. 111, No. 1 | 8 February 2021 Cross Ref Pressure and Equilibrium States in Ergodic TheoryEncyclopedia of Complexity and Systems Science | 26 January 2022 Cross Ref Uniqueness of Minimizer for Countable Markov Shifts and Equidistribution of Periodic PointsJournal of Statistical Physics, Vol. 181, No. 6 | 10 November 2020 Cross Ref On-the-fly closed-loop materials discovery via Bayesian active learningNature Communications, Vol. 11, No. 1 | 24 November 2020 Cross Ref Maximum and Shape of Interfaces in 3D Ising CrystalsCommunications on Pure and Applied Mathematics, Vol. 44 | 1 November 2020 Cross Ref Gibbs Variational Formula for Thermal Equilibrium States in Terms of Quantum Relative Entropy DensityJournal of Statistical Physics, Vol. 181, No. 3 | 3 July 2020 Cross Ref A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY -interactions on a Cayley treeJournal of Mathematical Physics, Vol. 61, No. 9 | 1 Sep 2020 Cross Ref Identities for Correlation Functions in Classical Statistical Mechanics and the Problem of Crystal StatesJournal of Statistical Physics, Vol. 180, No. 1-6 | 3 June 2020 Cross Ref Structure Learning of H-ColoringsACM Transactions on Algorithms, Vol. 16, No. 3 | 1 Jun 2020 Cross Ref Transport-information inequalities for Markov chainsThe Annals of Applied Probability, Vol. 30, No. 3 | 1 Jun 2020 Cross Ref Finitary codings for spatial mixing Markov random fieldsThe Annals of Probability, Vol. 48, N