Two‐dimensional continuum percolation and conduction

1984 ◽  
Vol 56 (3) ◽  
pp. 806-809 ◽  
Author(s):  
Mitsunobu Nakamura
Keyword(s):  
Continuum Percolation ◽  
Two Dimensional

Two‐dimensional continuum percolation and conduction. II

1985 ◽  
Vol 58 (9) ◽  
pp. 3499-3503 ◽  
Author(s):  
Mitsunobu Nakamura
Keyword(s):  
Continuum Percolation ◽  
Two Dimensional

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (2) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

scholarly journals Percolation in the signal to interference ratio graph

2006 ◽  
Vol 43 (02) ◽  
pp. 552-562 ◽  
Author(s):  
Olivier Dousse ◽  
Massimo Franceschetti ◽  
Nicolas Macris ◽  
Ronald Meester ◽  
Patrick Thiran
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Euclidean Distance ◽  
Critical Density ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Radio Communications ◽  
Communications Networks ◽  
Infinite Range ◽  
Independent Model

Continuum percolation models in which pairs of points of a two-dimensional Poisson point process are connected if they are within some range of each other have been extensively studied. This paper considers a variation in which a connection between two points depends not only on their Euclidean distance, but also on the positions of all other points of the point process. This model has been recently proposed to model interference in radio communications networks. Our main result shows that, despite the infinite-range dependencies, percolation occurs in the model when the density λ of the Poisson point process is greater than the critical density value λc of the independent model, provided that interference from other nodes can be sufficiently reduced (without vanishing).

Critical exponents of a two-dimensional continuum percolation system

1996 ◽  
Vol 54 (4) ◽  
pp. 3389-3392 ◽  
Author(s):  
A. Okazaki ◽  
K. Maruyama ◽  
K. Okumura ◽  
Y. Hasegawa ◽  
S. Miyazima
Keyword(s):  
Critical Exponents ◽  
Continuum Percolation ◽  
Two Dimensional
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