 |
|
|
| | | | | |
|
|
|
|
|
Transportation Approach to Some Concentration Inequalities in Product Spaces
|
Amir Dembo, Stanford University
Ofer Zeitouni, Technion - Israel Institute of Technology
|
Abstract
Let P be any product (Borel) probability measure on product (Polish) space E
and for vectors x,y,z in E let f(x,y,z) be the number of
coordinates k for which x_k neither equals y_k nor z_k.
Using a transportation approach we prove that
for every probability measure Q on E there exists a r.c.p.d. R such that
int R(.|x) dP(x) = Q(.)
and for every 0 < b < 1/2,
b b f(x,y,z)
int dP/dQ(y) dP/dQ(z) (1+b (1-2 b)) dR(y|x) dR(z|x) dP(x) =< 1
In the special case of Q(.)=P(.|A), with A a (measurable) subset of E,
we recover some of Talagrand's sharper concentration inequalities
in product spaces.
|
Full text: PDF
Pages: 83-90
Published on: October 24, 1996
|
Bibliography
- 1
-
Barbour A.D., Holst L. and Janson S. (1992),
Poisson approximation.
Oxford University Press, Oxford.
Math. Review 93g:60043
- 2
-
Bobkov S. and Ledoux M.
Poincar'e's inequalities and Talagrand's concentration phenomenon
for the exponential distribution.
1996 (preprint) Math. Review number not available.
- 3
-
Dembo, A.
Information inequalities and concentration of measure.
1996 (Ann. Probab. to appear) Math. Review number not available.
- 4
-
Dubins, L.E. (1962),
On extreme points of convex sets.
J. Math. Anal. Appl. 5, 237-244.
Math. Review 26:671
- 5
-
Ledoux M. (1996),
On Talagrand's deviation inequalities for product measures.
ESAIM: Probability and Statistics 1, 63-87.
Math. Review 1399224
- 6
-
Marton, K. (1986),
A simple proof of the blowing-up Lemma.
IEEE Trans. on Information Theory 32, 445-446.
Math. Review 87e:94018
- 7
-
Marton K. (1996),
Bounding dbar-distance by information divergence:
a method to prove measure concentration.
Ann. Probab. 24, 857-866.
Math. Review 1404531
- 8
-
Marton K. (1996),
A measure concentration inequality for contracting Markov chains.
GAFA 6, 556-571.
Math. Review 1392329
- 9
-
Talagrand, M. (1995),
Concentration of measure and isoperimetric inequalities in product spaces.
Publications Math'ematiques de l'I.H.E.S. 81, 73-205.
Math. Review 1361756
- 10
-
Talagrand M. (1996),
A new look at independence.
Ann. Probab. 24, 1-34.
Math. Review 1387624
- 11
-
Talagrand M.
New concentration inequalities in product spaces.
1996 (Invent. Math. to appear) Math. Review number not available.
- 12
-
Talagrand M. (1996),
Transportation cost for Gaussian and other product measures.
GAFA 6, 587-600.
Math. Review 1392331
|
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|
Context