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On a Property of Random-Oriented Percolation in a Quadrant

Dmitrii Zhelezov (Institutionen för matematiska vetenskaper, matematik)
Journal of Statistical Physics (0022-4715). Vol. 153 (2013), 5, p. 751-762.
[Artikel, refereegranskad vetenskaplig]

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 .

Nyckelord: Percolation, Random orientations, Phase transition



Denna post skapades 2013-12-10. Senast ändrad 2016-11-07.
CPL Pubid: 188744

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur