Bounding $\bar{d}$-distance by informational divergence: a method
to prove measure concentration
K. Marton
Source: Ann. Probab.
Volume 24, Number 2
(1996), 857-866.
Abstract
There is a simple inequality by Pinsker between variational distance
and informational divergence of probability measures defined on arbitrary
probability spaces. We shall consider probability measures on sequences taken
from countable alphabets, and derive, from Pinsker's inequality, bounds
on the $\bar{d}$-distance by informational divergence. Such bounds can be used
to prove the "concentration of measure" phenomenon for some
nonproduct distributions.
Primary Subjects: 60F10, 60G70, 60G05
Keywords: Measure concentration; isoperimetric inequality; Markov chains; $\bar{d}$-distance; informational divergence
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1039639365
Mathematical Reviews number (MathSciNet):
MR1404531
Digital Object Identifier: doi:10.1214/aop/1039639365
Zentralblatt MATH identifier:
0865.60017
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