Displaying similar documents to “Dynamical Percolation”

Dynamical sensitivity of the infinite cluster in critical percolation

Yuval Peres, Oded Schramm, Jeffrey E. Steif (2009)

Annales de l'I.H.P. Probabilités et statistiques

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In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has...

Near-minimal spanning trees : a scaling exponent in probability models

David J. Aldous, Charles Bordenave, Marc Lelarge (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We study the relation between the minimal spanning tree (MST) on many random points and the “near-minimal” tree which is optimal subject to the constraint that a proportion of its edges must be different from those of the MST. Heuristics suggest that, regardless of details of the probability model, the ratio of lengths should scale as 1+( ). We prove this in the model of the lattice with random edge-lengths and in the euclidean model.