### Skapa referens, olika format (klipp och klistra)

**Harvard**

Zhelezov, D. (2012) *On a property of random-oriented percolation in a quadrant*.

** BibTeX **

@unpublished{

Zhelezov2012,

author={Zhelezov, Dmitrii},

title={On a property of random-oriented percolation in a quadrant},

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 1/2. 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 $\mathbb{Z}^3$.},

year={2012},

keywords={percolation, random orientations, phase transition.},

note={11},

}

** RefWorks **

RT Unpublished Material

SR Electronic

ID 169492

A1 Zhelezov, Dmitrii

T1 On a property of random-oriented percolation in a quadrant

YR 2012

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 1/2. 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 $\mathbb{Z}^3$.

LA eng

LK http://arxiv.org/pdf/1205.5873v2.pdf

OL 30