Zobrazeno 1 - 10
of 108
pro vyhledávání: '"Fradelizi, Matthieu"'
Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santal\'o inequality in its functional form. Inspired by their method, based on the Fokker-Planck sem
Externí odkaz:
http://arxiv.org/abs/2409.05541
In a recent work, Bo'az Klartag showed that, given a convex body with minimal volume product, its isotropic constant is related to its volume product. As a consequence, he obtained that a strong version of the slicing conjecture implies Mahler's conj
Externí odkaz:
http://arxiv.org/abs/2406.07406
In "Weighted Brunn-Minkowski Theory I", the prequel to this work, we discussed how recent developments on concavity of measures have laid the foundations of a nascent weighted Brunn-Minkowski theory. In particular, we defined the mixed measures of th
Externí odkaz:
http://arxiv.org/abs/2402.10314
Caffarelli's contraction theorem states that probability measures with uniformly logconcave densities on R d can be realized as the image of a standard Gaussian measure by a globally Lipschitz transport map. We discuss some counterexamples and obstru
Externí odkaz:
http://arxiv.org/abs/2402.04649
We prove the following type of discrete entropy monotonicity for sums of isotropic, log-concave, independent and identically distributed random vectors $X_1,\dots,X_{n+1}$ on $\mathbb{Z}^d$: $$ H(X_1+\cdots+X_{n+1}) \geq H(X_1+\cdots+X_{n}) + \frac{d
Externí odkaz:
http://arxiv.org/abs/2401.15462
We explore alternative functional or transport-entropy formulations of the Blaschke-Santal{\'o} inequality and of its conjectured counterpart due to Mahler. In particular, we obtain new direct and reverse Blaschke-Santal{\'o} inequalities for s-conca
Externí odkaz:
http://arxiv.org/abs/2307.04393
Our purpose here is to give an overview of known results and open questions concerning the volume product ${\mathcal P}(K)=\min_{z\in K}{\rm vol}(K){\rm vol}((K-z)^*)$ of a convex body $K$ in ${\mathbb R}^n$. We present a number of upper and lower bo
Externí odkaz:
http://arxiv.org/abs/2301.06131
Publikováno v:
Journal of Mathematical Analysis and Applications, Vol. 529, No. 2, January 2024
The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of these concepts to Borel measures with density in $\mathbb{R}^n$-- in parti
Externí odkaz:
http://arxiv.org/abs/2212.13522
Publikováno v:
Journal of Functional Analysis, Vol. 286, No. 3, February 2024
We explore some inequalities in convex geometry restricted to the class of zonoids. We show the equivalence, in the class of zonoids, between a local Alexandrov-Fenchel inequality, a local Loomis-Whitney inequality, the log-submodularity of volume, a
Externí odkaz:
http://arxiv.org/abs/2206.02123
Sumset estimates, which provide bounds on the cardinality of sumsets of finite sets in a group, form an essential part of the toolkit of additive combinatorics. In recent years, probabilistic or entropic analogs of many of these inequalities were int
Externí odkaz:
http://arxiv.org/abs/2206.01565