Results 1 to 10 of about 427 (24)
The dimension of the Incipient Infinite Cluster [PDF]
, 2014 We study the Incipient Infinite Cluster (IIC) of high-dimensional bond percolation on $\mathbb{Z}^d$. We prove that the mass dimension of IIC almost surely equals $4$ and the volume growth exponent of IIC almost surely equals $2$.Comment: 9 ...
van Batenburg, Wouter Cames
core +15 more sources
Forum of Mathematics, Pi, 2017 Conformal loop ensembles (CLEs) are random collections of loops in a simply connected domain, whose laws are characterized by a natural conformal invariance property.
JASON MILLER +2 more
doaj +1 more source
Multiple geodesics with the same direction [PDF]
, 2011 The directed last-passage percolation (LPP) model with independent exponential times is considered. We complete the study of asymptotic directions of infinite geodesics, started by Ferrari and Pimentel \cite{FP}.
Coupier, David
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First-passage percolation with exponential times on a ladder [PDF]
, 2010 We consider first-passage percolation on a ladder, i.e. the graph {0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to calculate an explicit expression
Renlund, Henrik
core +1 more source
Percolation of hard disks [PDF]
, 2013 Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process.
D. Aristoff, Daley
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Moderate deviations for the chemical distance in Bernoulli percolation [PDF]
, 2009 In this paper, we establish moderate deviations for the chemical distance in Bernoulli percolation. The chemical distance between two points is the length of the shortest open path between these two points.
Garet, Olivier, Marchand, Régine
core +5 more sources
Percolation-induced exponential scaling in the large current tails of random resistor networks [PDF]
, 2013 There is a renewed surge in percolation-induced transport properties of diverse nano-particle composites (cf. RSC Nanoscience & Nanotechnology Series, Paul O'Brien Editor-in-Chief).
Forest, M. Gregory +3 more
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Counting minimal cutsets and $p_c<1$
Forum of Mathematics, PiWe prove two results concerning percolation on general graphs. • We establish the converse of the classical Peierls argument: if the critical parameter for (uniform) percolation satisfies ...
Philip Easo +2 more
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No directed fractal percolation in zero area
, 1997 We show that fractal (or "Mandelbrot") percolation in two dimensions produces a set containing no directed paths, when the set produced has zero area. This improves a similar result by the first author in the case of constant retention probabilities to ...
B. Duplantier +8 more
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Four universal growth regimes in degree-dependent first passage percolation on spatial random graphs
Forum of Mathematics, SigmaOne-dependent first passage percolation is a spreading process on a graph where the transmission time through each edge depends on the direct surroundings of the edge. In particular, the classical i.i.d. transmission time $L_{xy}$ is multiplied by
Júlia Komjáthy +3 more
doaj +1 more source