{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:06:34Z","timestamp":1770980794968,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and  $0  &lt;  p  &lt;  \\infty$. This complements earlier results by Heinrich, Novak, Wasilkowski &amp; Wo\u017ania-kowski,  Hinrichs  &amp; 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.<\/jats:p>","DOI":"10.37236\/378","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:11:02Z","timestamp":1578715862000},"source":"Crossref","is-referenced-by-count":9,"title":["The Asymptotic Behavior of the Average $L^p-$Discrepancies and a Randomized Discrepancy"],"prefix":"10.37236","volume":"17","author":[{"given":"Stefan","family":"Steinerberger","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2010,8,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r106\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r106\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:28:12Z","timestamp":1579303692000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/378","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8,9]]},"article-number":"R106"}}