Geodesic
The asymptotic behavior of the average \(L^p\)-discrepancies and a randomized discrepancy
The electronic journal of combinatorics, Tome 17 (2010)
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This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and $0 < p < \infty$. This complements earlier results by Heinrich, Novak, Wasilkowski & Woźnia-kowski, Hinrichs & Novak and Gnewuch and proves that the hitherto best known upper bounds are optimal up to constants.We furthermore introduce a new discrepancy $D_{N}^{\mathbb{P}}$ by taking a probabilistic approach towards the extreme discrepancy $D_{N}$. We show that it can be interpreted as a centralized $L^1-$discrepancy $D_{N}^{(1)}$, provide upper and lower bounds and prove a limit theorem.
DOI : 10.37236/378
Classification : 11K06, 11K38, 60D05
Mots-clés : discrepancy, average \(L^p\) discrepancy 
@article{10_37236_378,
     author = {Stefan Steinerberger},
     title = {The asymptotic behavior of the average {\(L^p\)-discrepancies} and a randomized discrepancy},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/378},
     zbl = {1217.11072},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/378/}
}
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Stefan Steinerberger. The asymptotic behavior of the average \(L^p\)-discrepancies and a randomized discrepancy. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/378

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