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Limit theorems for the minimum interpoint distance between any pair of i.i.d. random points in R d |
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| Authors: | S Kanagawa Y Mochizuki H Tanaka |
| Institution: | (1) Department of Mathematics, Yamanashi University, Takeda, 400 Kofu, Japan;(2) Matsushita Electric Industrial CO. LTD., 1006 Oaza-Kadoma, 571 Kadoma, Osaka, Japan;(3) Department of Mathematics, Faculty of Science and Technology, Keio University, Kohoku-ku, 223 Yokohama, Kanagawa, Japan |
| Abstract: | The limit theorem for the minimum interpoint distance between any pair of i.i.d. random points in R
d
with common density f L
2 was studied by a method which makes use of the convergence of point processes. Some one-dimensional examples with f L
2 (including the cases Beta and Gamma distributions) were also considered. |
| Keywords: | Minimum interpoint distance Poisson point process compensator Skorohod J 1-topology |
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