Percolation Theory and First-Passage Percolation
نویسندگان
چکیده
منابع مشابه
Monotonicity 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 کاملFirst passage percolation on the random graph
We study first passage percolation on the random graph Gp(N) with exponentially distributed weights on the links. For the special case of the complete graph this problem can be described in terms of a continuous time Markov chain and recursive trees. The Markov chain X(t) describes the number of nodes that can be reached from the initial node in time t. The recursive trees, which are uniform tr...
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: The Annals of Probability
سال: 1987
ISSN: 0091-1798
DOI: 10.1214/aop/1176991975