A Lower Bound for the Discrepancy of a Random Point Set
نویسنده
چکیده
We show that there are constants k,K > 0 such that for all N, s ∈ N, s ≤ N , the point set consisting of N points chosen uniformly at random in the s-dimensional unit cube [0, 1]s with probability at least 1− e−ks admits an axis-parallel rectangle [0, x] ⊆ [0, 1]s containing K √ sN points more than expected. Consequently, the expected star discrepancy of a random point set is of order √
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ورودعنوان ژورنال:
- J. Complexity
دوره 30 شماره
صفحات -
تاریخ انتشار 2014