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- W4242848119 abstract "Let denote a rectangular lattice in the Euclidean plane E 2 , generated by ( a × b ) rectangles. In this paper we consider the probability that a random ellipse having main axes of length 2 α and 2 ß , with intersects . We regard the lattice as the union of two orthogonal sets and of equidistant lines and evaluate the probability that the random ellipse intersects or . Moreover, we consider the dependence structure of the events that the ellipse intersects or . We study further the case when the main axes of the ellipse are parallel to the lines of the lattice and satisfy 2 ß = min ( a, b ) < 2 α = max ( a, b ). In this case, the probability of intersection is 1, and there exist almost surely two perpendicular segments in within the ellipse. We evaluate the distribution function, density, mean and variance of the length of these segments. We conclude with a generalization of this problem in three dimensions." @default.
- W4242848119 created "2022-05-12" @default.
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- W4242848119 date "1993-12-01" @default.
- W4242848119 modified "2023-10-18" @default.
- W4242848119 title "Hitting probabilities for random ellipses and ellipsoids" @default.
- W4242848119 cites W2018218999 @default.
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- W4242848119 doi "https://doi.org/10.1017/s0021900200044703" @default.
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