منابع مشابه
The frog model with drift on R
Consider a Poisson process on R with intensity f where 0 ≤ f(x) <∞ for x ≥ 0 and f(x) = 0 for x < 0. The “points” of the process represent sleeping frogs. In addition, there is one active frog initially located at the origin. At time t = 0 this frog begins performing Brownian motion with leftward drift λ (i.e. its motion is a random process of the form Bt − λt). Any time an active frog arrives ...
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On the range of the transient frog model on Z
In this paper, we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for the moments of the lower bound of the model’s long-run range, as well as their asymptotic limits as the drift of the underlying random walk vanishes. We al...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2017
ISSN: 1083-589X
DOI: 10.1214/17-ecp61