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Isoperimetric Constants for Product Probability Measures
(Georgia Institute of Technology, 1995-07-24)
A dimension free lower bound is found for isoperimetric constants
of product probability measures. From this, some analytic inequalities
are derived.
Sharp Constants in Some Multiplicative Sobolev Inequalities
(Georgia Institute of Technology, 1995-09-16)
The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities ...
Dimension Free Weak Concentration of Measure Phenomenon
(Georgia Institute of Technology, 1995-07-24)
For product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form
\mu^n (A + h[-1,1]^n)\ge R_h(\mu^n(A)) to hold; for a ...
Variance of Lipschitz Functions and an Isoperimetric Problem for a Class of Product Measures
(Georgia Institute of Technology, 1995-07-10)
The maximal variance of Lipschitz functions (with respect to the
\ell_1-distance) of independent random vectors is found. This is then used
to solve the isoperimetric problem, uniformly in the class of product
probability ...
A Characterization of Gaussian Measures via the Isoperimetric Property of Half-Spaces
(Georgia Institute of Technology, 1995-07-25)
If the half-spaces of the form {x\in R^n: x_1 \le c} are extremal in
the isoperimetric problem for the product measure \mu^n, n\ge 2, then
\mu is Gaussian.