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- W2002730003 abstract "Let C be a planar region. Choose n points p 1 ,⋯,p n I.I.D. from the uniform distribution over C . Let M C n be the number of these points that are maximal. If C is convex it is known that either E( M C n )= Θ (√ n )> or E( M C n )=O( log n ). In this paper we will show that, for general C , there is very little that can be said, a-priori, about E( M C n ). More specifically we will show that if g is a member of a large class of functions then there is always a region C such that E( M C n )= Θ ( g ( n )). This class contains, for example, all monotically increasing functions of the form g ( n )= n α ln β n , where 0< α <1 and β ⩾0. This class also contains nondecreasing functions like g(n)=ln ∗ n . The results in this paper remain valid in higher dimensions." @default.
- W2002730003 created "2016-06-24" @default.
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- W2002730003 date "1993-04-01" @default.
- W2002730003 modified "2023-09-27" @default.
- W2002730003 title "How many maxima can there be?" @default.
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- W2002730003 doi "https://doi.org/10.1016/0925-7721(93)90014-w" @default.
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