Local functional inequalities in one-dimensional free probability

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• 作者：Ionel Popescu^a ; ^b ; ^{ipopescu@math.gatech.edu}
• 关键词：Free probability ; Functional inequalities
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：15 March, 2013
• 年：2013
• 卷：264
• 期：6
• 页码：1456-1479
• 全文大小：235 K

文摘

In this note we introduce and prove local and potential independent transportation, Log-Sobolev and HWI inequalities in one-dimensional free probability on compact intervals which are sharp. We recover using this approach a free transportation inequality on the whole real line which was put forward recently by Ma?da and Maurel-Segala (2012) . Our method is based on the operator theoretic approach developed by Ledoux and Popescu to deal with the free Poincar¨¦ inequality.