Now showing items 1-5 of 5

• #### 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.
• #### 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 ...
• #### 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 ...
• #### 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 ...