Probabilistic star discrepancy bounds for double infinite random matrices
نویسندگان
چکیده
In 2001 Heinrich, Novak, Wasilkowski and Woźniakowski proved that the inverse of the discrepancy depends linearly on the dimension, by showing that a Monte Carlo point set P of N points in the s-dimensional unit cube satisfies the discrepancy bound D∗s N (P)≤ cabssN with positive probability. Later their results were generalized by Dick to the case of double infinite random matrices. In the present paper we give asymptotically optimal bounds for the discrepancy of such random matrices, and give estimates for the corresponding probabilities. Additionally, we show how our results can be applied to Markov Chain Monte Carlo.
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تاریخ انتشار 2012