Disjoint crossings, positive speed and deviation estimates for first passage percolation
نویسندگان
چکیده
منابع مشابه
Disjoint crossings, positive speed and deviation estimates for first passage percolation
Consider bond percolation on the square latticeZ where each edge is independently open with probability p. For some positive constants p0 ∈ (0, 1), 1 and 2, the following holds: if p > p0, then with probability at least 1− 1 n4 there are at least 2n logn disjoint open left-right crossings in Bn := [0, n] 2 each having length at most 2n, for all n ≥ 2. Using the proof of the above, we obtain pos...
متن کاملMonotonicity in first-passage percolation
We consider standard first-passage percolation on Zd. Let e1 be the first coordinate vector. Let a(n) be the expected passage time from the origin to ne1. In this short paper, we note that a(n) is increasing under some strong condition on the support of the distribution of the passage times on the edges.
متن کاملGeodesics in First-Passage Percolation
We consider a wide class of ergodic first passage percolation processes on Z2 and prove that there exist at least four one-sided geodesics a.s. We also show that coexistence is possible with positive probability in a four color Richardson’s growth model. This improves earlier results of Häggström and Pemantle [9], Garet and Marchand [7] and Hoffman [11] who proved that first passage percolation...
متن کاملBatch queues, reversibility and first-passage percolation
We consider a model of queues in discrete time, with batch services and arrivals. The case where arrival and service batches both have Bernoulli distributions corresponds to a discrete-time M/M/1 queue, and the case where both have geometric distributions has also been previously studied. We describe a common extension to a more general class where the batches are the product of a Bernoulli and...
متن کاملFirst-passage percolation on width-two stretches
In this work we consider two first-passage percolation problems. In the first part we concern ourselves with effectively one-dimensional graphs with vertex set {1 . . . , n}×{0, 1} and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate χ by solving certain recursive distributional equations and invoking result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2014
ISSN: 1083-589X
DOI: 10.1214/ecp.v19-3490