Results 11 to 20 of about 427 (24)
A short proof of the phase transition for the vacant set of random interlacements [PDF]
, 2015 The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories, where $u$ is a ...
Rath, Balazs
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Contact process under renewals I
, 2018 Motivated by questions regarding long range percolation, we investigate a non-Markovian analogue of the Harris contact process in $\mathbb{Z}^d$: an individual is attached to each site $x \in \mathbb{Z}^d$, and it can be infected or healthy; the ...
Fontes, Luiz Renato G. +3 more
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Subcritical regimes in the Poisson Boolean model of continuum percolation
, 2008 We consider the Poisson Boolean model of continuum percolation. We show that there is a subcritical phase if and only if $E(R^d)$ is finite, where $R$ denotes the radius of the balls around Poisson points and $d$ denotes the dimension.
Gouéré, Jean-Baptiste
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Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$
, 2017 We consider bond percolation on $\Z^d\times \Z^s$ where edges of $\Z^d$ are open with probability ...
Sanchis, Rémy, Silva, Roger W. C.
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Continuum percolation with steps in an annulus
, 2004 Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-\epsilon) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1 and let G_A be the random graph with vertex set {x_i} and edges ...
Balister, Paul +2 more
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Brownian Web and Oriented Percolation: Density Bounds [PDF]
, 2011 In a recent work, we proved that under diffusive scaling, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2 converges in distribution to the Brownian web.
Sarkar, Anish, Sun, Rongfeng
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The two-type Richardson model with unbounded initial configurations
, 2007 The two-type Richardson model describes the growth of two competing infections on $\mathbb{Z}^d$ and the main question is whether both infection types can simultaneously grow to occupy infinite parts of $\mathbb{Z}^d$. For bounded initial configurations,
Deijfen, Maria, Häggström, Olle
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Continuity of the asymptotic shape of the supercritical contact process
, 2015 We prove the continuity of the shape governing the asymptotic growth of the supercritical contact process in Z^d , with respect to the infection parameter.
Garet, Olivier +2 more
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Critical random graphs: Diameter and mixing time
, 2008 Let $\mathcal{C}_1$ denote the largest connected component of the critical Erd\H{o}s--R\'{e}nyi random graph $G(n,{\frac{1}{n}})$. We show that, typically, the diameter of $\mathcal{C}_1$ is of order $n^{1/3}$ and the mixing time of the lazy simple ...
Nachmias, Asaf, Peres, Yuval
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First passage percolation and a model for competing spatial growth
, 1996 We generalize Richardson's model by starting with two sites of different colors and giving each new site the color of the site that spawned it.
Haggstrom, Olle, Pemantle, Robin
core