کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4592449 1335101 2009 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Mass transportation proofs of free functional inequalities, and free Poincaré inequalities
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Mass transportation proofs of free functional inequalities, and free Poincaré inequalities
چکیده انگلیسی

This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the transportation, Log-Sobolev, HWI interpolation and Brunn–Minkowski inequalities for strictly convex potentials. Sharp constants and some extended versions are put forward. The paper also addresses two versions of free Poincaré inequalities and their interpretation in terms of spectral properties of Jacobi operators. The last part establishes the corresponding inequalities for measures on R+ with the reference example of the Marcenko–Pastur distribution.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 257, Issue 4, 15 August 2009, Pages 1175-1221