Continuum Percolation

By I. Balberg. Encyclopedia of Complexity and Systems Science, 2009

647 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/15c9f294d8d1b820f7a30f9c96b2674dd67c6194

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In Condensed Matter Physics

In Materials Chemistry

In Mathematical Physics

Citations in the corpus

The topology of probability distributions on manifolds (2013, result): “There is a natural connection of the results in this paper with results in point processes, specifically random set models such as the Poisson-Boolean model [37].”
Stochastic geometry and random graphs for the analysis and design of wireless networks (2009, background): “Gilbert’s original model has undergone many generalizations, and continuum percolation theory is now a rich mathematical ﬁ eld, see [2], [35].”
Scale-free percolation (2011, neutral): “A continuum analogue of long-range percolation, known as the random connection model, is described in [27].”
Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory (2007, background): “Percolation theory [9], [15] is a field of mathematics and statistical physics that provides models of phase transition phenomena that are observed in nature.”
Sampling-based algorithms for optimal motion planning (2011, background): “In other words, for all λ > λc, there is a non-zero probability that the origin is in an infinite connected component of Gdisc∞ ( λ, 1); moreover, under these conditions, the graph has precisely one infinite connected component, almost surely (Meester and Roy 1996).”
Gaussian Limts for Random Geometric Measures (2007, background): “1 Germ-grain models Germ-grain models are a fundamental model of random sets in stochastic geometry; see for example (9; 15; 26).”
Conformal loop ensembles: the Markovian characterization and the loop-soup construction (2010, background): “Note that the standard arguments developed in the context of Mandelbrot percolation (see [23], [6]) can be easily adapted to the present setting in order to prove that c0 is subcritical, but not in the sense we have defined it.”
CONNECTIVITY OF SOFT RANDOM GEOMETRIC GRAPHS (2013, background): “Soft random geometric graphs of this type are a finite-space version of the socalled random connection model of continuum percolation; see [11, 13], which describe further motivation, and see [11, Section 1.”
Insertion and deletion tolerance of point processes (2010, background): “The Boolean continuum percolation model for point processes is defined as follows (see [19]).”
Recurrence versus transience for weight-dependent random connection models (2019, methodology): “For further constructions, see Last and Ziesche [25] and Meester and Roy [28].”
Random geometric complexes in the thermodynamic regime (2014, methodology): “We start with some definitions from percolation theory for the Boolean model on Poisson processes ([24]) needed for the proof of the Poisson central limit theorem.”
Second-order properties and central limit theorems for geometric functionals of Boolean models (2013, background): “This is a fundamental model of stochastic geometry and continuum percolation with many applications in materials science and physics [3, 7, 17, 20, 28].”
A parsimonious model of mobile partitioned networks with clustering (2009, background): “The region A l can be generated, for example, as the union of m random disks ofradius rl, and Ah its complement (cf. Figure 1). where: • Z (0) is an initial position in the torus; • Zx and Zy satisfies the following conditions: (4)”
Poisson process Fock space representation, chaos expansion and covariance inequalities (2009, background): “In Section 5 we prove some results on covariances, including the following HarrisFKG inequality; see also [26], [4] (treating special Poisson processes) [43], and [9] for more general point processes.”