Extremal Properties of Central Half - Spacesfor Product
نویسنده
چکیده
We deal with the isoperimetric and the shift problem for subsets of measure one half in product probability spaces. We prove that the canonical central half-spaces are extremal in particular cases: products of log-concave measures on the real line satisfying precise conditions and products of uniform measures on spheres, or balls. As a corollary, we improve the known log-Sobolev constants for Euclidean balls. We also give some new results about the related question of estimating the volume of sections of unit balls of`p-sums of Minkowski spaces.
منابع مشابه
Hyperinvariant subspaces and quasinilpotent operators
For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors. We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors. Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector, and so $T$ has a nontrivial hyperinvariant subspace.
متن کاملAZ-Identities and Strict 2-Part Sperner Properties of Product Posets
One of central issues in extremal set theory is Sperner's theorem and its generalizations. Among such generalizations is the best-known BLYM inequality and the Ahlswede--Zhang (AZ) identity which surprisingly generalizes the BLYM into an identity. Sperner's theorem and the BLYM inequality has been also generalized to a wide class of posets. Another direction in this research was the study of mo...
متن کاملExtremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
We study correlation functions of single-cycle chiral operators in Sym T 4, the symmetric product orbifold of N supersymmetric four-tori. Correlators of twist operators are evaluated on covering surfaces, generally of different genera, where fields are single-valued. We compute some simple four-point functions and study how the sum over inequivalent branched covering maps splits under OPEs. We ...
متن کاملCharacterization and Estimation of the Multivariate Extremal Index
The multivariate extremal index has been introduced by Nandagopalan as a measure of the clustering among the extreme values of a multivariate stationary process. In this paper, we derive some additional properties and use those to construct a statistical estimation scheme. Central to the discussion is a class of processes we call M 4 processes, which are characterized by means of a multivariate...
متن کامل