Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its Subgraphs

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Previous article Next article Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its SubgraphsM. V. Men’shikovM. V. Men’shikovhttps://doi.org/10.1137/1132082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. V. Men'shikov, , S. A. Molchanov and , A. F. Sidorenko, Percolation theory and some applicationsProbability theory. Mathematical statistics. Theoretical cybernetics, Vol. 24 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986, 53–110, i, in Progress in Science and Technology, Ser., (In Russian.) 88m:60273 Google Scholar[2] Harry Kesten, Percolation theory for mathematicians, Progress in Probability and Statistics, Vol. 2, Birkhäuser Boston, Mass., 1982iv+423 84i:60145 0522.60097 CrossrefGoogle Scholar[3] M. V. Men'shikov, Coincidence of critical points in percolation problems, Soviet Math. Dokl., 33 (1986), 856–859 0615.60096 Google Scholar[4] S. A. Zuev, Bounds for the percolation threshold for a square lattice, Theory Probab. Appl., 32 (1987), 551–553 10.1137/1132084 0677.60108 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Strict inequality for bond percolation on a dilute lattice with columnar disorderStochastic Processes and their Applications, Vol. 149 Cross Ref The symbiotic contact processElectronic Journal of Probability, Vol. 25, No. none Cross Ref Strict Inequalities of Critical Values in Continuum Percolation20 January 2011 | Journal of Statistical Physics, Vol. 142, No. 3 Cross Ref Multiscale percolation on k-symmetric mosaicStatistics & Probability Letters, Vol. 52, No. 1 Cross Ref Mixed percolation as a bridge between site and bond percolationThe Annals of Applied Probability, Vol. 10, No. 4 Cross Ref Critical probabilities for site and bond percolation modelsThe Annals of Probability, Vol. 26, No. 4 Cross Ref Percolation and disordered systems11 October 2006 Cross Ref Comparison and disjoint-occurrence inequalities for random-cluster modelsJournal of Statistical Physics, Vol. 78, No. 5-6 Cross Ref Potts models and random-cluster processes with many-body interactionsJournal of Statistical Physics, Vol. 75, No. 1-2 Cross Ref Strict inequality for critical values of Potts models and random-cluster processesCommunications in Mathematical Physics, Vol. 158, No. 1 Cross Ref Differential Inequalities for Potts and Random-Cluster Processes Cross Ref On the geometry of random Cantor sets and fractal percolationJournal of Theoretical Probability, Vol. 5, No. 3 Cross Ref Strict monotonicity for critical points in percolation and ferromagnetic modelsJournal of Statistical Physics, Vol. 63, No. 5-6 Cross Ref The Coincidence of Critical Points in Poisson Percolation ModelsM. V. Men’shikov and A. F. Sidorenko17 July 2006 | Theory of Probability & Its Applications, Vol. 32, No. 3AbstractPDF (471 KB) Volume 32, Issue 3| 1988Theory of Probability & Its Applications History Submitted:16 April 1986Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1132082Article page range:pp. 544-547ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics