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Disjoint crossings, positive speed and deviation estimates for first passage percolation

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1.	Title	Title of document	Disjoint crossings, positive speed and deviation estimates for first passage percolation
2.	Creator	Author's name, affiliation, country	Ghurumuruhan Ganesan; École Polytechnique Fédérale de Lausanne; Switzerland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	Consider bond percolation on the square lattice \(\mathbb{Z}^2\) where each edge is independently open with probability \(p.\) For some positive constants \(p_0 \in (0,1), \epsilon_1\) and \(\epsilon_2,\) the following holds: if \(p > p_0,\) then with probability at least \(1-\frac{\epsilon_1}{n^{4}}\) there are at least \(\frac{\epsilon_2 n}{\log{n}}\) disjoint open left-right crossings in \(B_n := [0,n]^2\) each having length at most \(2n,\) for all \(n \geq 2.\) Using the proof of the above, we obtain positive speed for first passage percolation with independent and identically distributed edge passage times \(\{t(e_i)\}_i\) satisfying \(\mathbb{E}\left(\log{t(e_1)}\right)^+<\infty;\) namely, \(\limsup_n \frac{T_{pl}(0,n)}{n} \leq Q\) a.s. for some  constant \(Q < \infty,\) where \(T_{pl}(0,n)\) denotes the minimum passage time from the point \((0,0)\) to the line \(x=n\) taken over all paths contained in \(B_n.\) Finally, we also obtain deviation corresponding estimates for nonidentical passage times satisfying \(\inf_i\mathbb{P}(t(e_i) = 0) > \frac{1}{2}.\)
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2014-08-11
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/3490
10.	Identifier	Digital Object Identifier	10.1214/ECP.v19-3490
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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