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**Harvard**

Zhelezov, D. (2013) *On a Property of Random-Oriented Percolation in a Quadrant*.

** BibTeX **

@article{

Zhelezov2013,

author={Zhelezov, Dmitrii},

title={On a Property of Random-Oriented Percolation in a Quadrant},

journal={Journal of Statistical Physics},

issn={0022-4715},

volume={153},

issue={5},

pages={751-762},

abstract={Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability p and leftwards (resp. downwards) otherwise. We consider a variation of Grimmett's model proposed by Hegarty, in which edges are oriented away from the origin with probability p, and towards it with probability 1-p, which implies rotational instead of translational symmetry. We show that both models could be considered as special cases of random-oriented percolation in the NE-quadrant, provided that the critical value for the latter is . As a corollary, we unconditionally obtain a non-trivial lower bound for the critical value of Hegarty's random-orientation model. The second part of the paper is devoted to higher dimensions and we show that the Grimmett model percolates in any slab of height at least 3 in .},

year={2013},

keywords={Percolation, Random orientations, Phase transition },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 188744

A1 Zhelezov, Dmitrii

T1 On a Property of Random-Oriented Percolation in a Quadrant

YR 2013

JF Journal of Statistical Physics

SN 0022-4715

VO 153

IS 5

SP 751

OP 762

AB Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability p and leftwards (resp. downwards) otherwise. We consider a variation of Grimmett's model proposed by Hegarty, in which edges are oriented away from the origin with probability p, and towards it with probability 1-p, which implies rotational instead of translational symmetry. We show that both models could be considered as special cases of random-oriented percolation in the NE-quadrant, provided that the critical value for the latter is . As a corollary, we unconditionally obtain a non-trivial lower bound for the critical value of Hegarty's random-orientation model. The second part of the paper is devoted to higher dimensions and we show that the Grimmett model percolates in any slab of height at least 3 in .

LA eng

DO 10.1007/s10955-013-0856-z

LK http://dx.doi.org/10.1007/s10955-013-0856-z

OL 30