Critical path analysis for continuum percolation
Jiří Černý (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Jiří Černý (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Marie Théret (2008)
Annales de la faculté des sciences de Toulouse Mathématiques
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We consider the standard first passage percolation on : with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten proved in 1987 a law of large numbers for the rescaled flow. Chayes and Chayes established that the large deviations far away below its typical value are of surface order, at least for the Bernoulli percolation and cylinders of certain height. Thanks to another approach...
Emilio De Santis (2002)
Annales de l'I.H.P. Probabilités et statistiques
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Pete, Gabor (2008)
Electronic Communications in Probability [electronic only]
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Christoph Bandt, T. Retta (1992)
Fundamenta Mathematicae
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Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, "fractal structure" is not a metric but a topological phenomenon.
Olle Häggström, Yuval Peres, Jeffrey E. Steif (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Coloma Ballester, Vicent Caselles (2001)
Publicacions Matemàtiques
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We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain Ω' of the image is Jordan domain, a rectangle, for instance,...