location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword Brascamp-Lieb inequality

 Expand all        Collapse all Results 1 - 3 of 3

1. CJM Online first

Colesanti, Andrea; Gómez, Eugenia Saorín; Nicolás, Jesus Yepes
 On a linear refinement of the PrÃ©kopa-Leindler inequality If $f,g:\mathbb{R}^n\longrightarrow\mathbb{R}_{\geq0}$ are non-negative measurable functions, then the PrÃ©kopa-Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater or equal than the $0$-mean of the integrals of $f$ and $g$. In this paper we prove that under the sole assumption that $f$ and $g$ have a common projection onto a hyperplane, the PrÃ©kopa-Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality. Keywords:PrÃ©kopa-Leindler inequality, linearity, Asplund sum, projections, Borell-Brascamp-Lieb inequalityCategories:52A40, 26D15, 26B25

2. CJM Online first

Cordero-Erausquin, Dario
 Transport inequalities for log-concave measures, quantitative forms and applications We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure. We discuss quantitative forms of these inequalities, with application to the variance Brascamp-Lieb inequality. Keywords:log-concave measures, transport inequality, Brascamp-Lieb inequality, quantitative inequalitiesCategories:52A40, 60E15, 49Q20

3. CJM 2010 (vol 62 pp. 870)

 The Brascamp-Lieb Polyhedron A set of necessary and sufficient conditions for the Brascamp--Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank $1$. This complements the result of Barthe concerning the case where the linear maps all have rank $1$. Pushing our analysis further, we describe the case where the maps have either rank $1$ or rank $2$. A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp--Lieb inequality to hold. We present an algorithm which generates such a list. Keywords:Brascamp-Lieb inequality, Loomis-Whitney inequality, lattice, flagCategories:44A35, 14M15, 26D20