Large deviations of convex hulls of planar random walks and Brownian motions
نویسندگان
چکیده
We prove large deviations principles (LDPs) for the perimeter and area of convex hull a planar random walk with finite Laplace transform its increments.
منابع مشابه
Convex hulls of random walks: Large-deviation properties.
We study the convex hull of the set of points visited by a two-dimensional random walker of T discrete time steps. Two natural observables that characterize the convex hull in two dimensions are its perimeter L and area A. While the mean perimeter 〈L〉 and the mean area 〈A〉 have been studied before, analytically and numerically, and exact results are known for large T (Brownian motion limit), li...
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Let Sk be a random walk in R such that its distribution of increments does not assign mass to hyperplanes. We study the probability pn that the convex hull conv(S1, . . . , Sn) of the first n steps of the walk does not include the origin. By providing an explicit formula, we show that for planar symmetrically distributed random walks, pn does not depend on the distribution of increments. This e...
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We give an explicit formula for the probability that the convex hull of an n-step random walk in R does not contain the origin, under the assumption that the distribution of increments of the walk is centrally symmetric and puts no mass on affine hyperplanes. This extends the formula by Sparre Andersen (Skand Aktuarietidskr 32:27–36, 1949) for the probability that such random walk in dimension ...
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This paper is based on two talks given by the author in the Albany meeting in the summer of 1997. The rst of these, which dealt with perturbed Brownian motion and random walk, is discussed in Section 1, and the second, which involved Brownian local times, is the subject of Section 2.
متن کاملPerturbed Random Walks and Brownian Motions, and Local Times
This paper is based on two talks given by the author in the Albany meeting in the summer of The rst of these which dealt with perturbed Brownian motion and random walk is discussed in Section and the second which involved Brownian local times is the subject of Section
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ژورنال
عنوان ژورنال: Annales Henri Lebesgue
سال: 2021
ISSN: ['2644-9463']
DOI: https://doi.org/10.5802/ahl.100