On the small ball inequality in three dimensions
نویسندگان
چکیده
منابع مشابه
On the Small Ball Inequality in All Dimensions
The point of interest is the dependence upon the logarithm of the volume of the rectangles. With n(d−1)/2 on the left above, the inequality is trivial, while it is conjectured that the inequality holdswith n(d−2)/2. This is known in the case of d = 2 (Talagrand, 1994), and a recent paper of two of the authors (Bilyk and Lacey, 2006) proves a partial result towards the conjecture in three dimens...
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The question of obtaining more precise information about the term o(l) in (3) seems to have been first publicly raised by W. W. Sawyer [ l ] . Because of the interest of this problem in numerical analysis [2] it has been investigated by several workers [3; 4; 5] with the result that various upper and lower bounds for the rate of growth of this term are known. We have been able to determine the ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2008
ISSN: 0012-7094
DOI: 10.1215/00127094-2008-016