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Transportation Approach to Some Concentration Inequalities in Product Spaces

   
@article{ECP979,
	author = {Amir Dembo and Ofer Zeitouni},
	title = {Transportation Approach to Some Concentration Inequalities in Product Spaces},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {1},
	year = {1996},
	keywords = {Concentration inequalities, product spaces, transportation.},
	abstract = {Using a transportation approach we prove that for every probability measures $P,Q_1,Q_2$ on $\Omega^N$ with $P$ a product measure there exist r.c.p.d. $\nu_j$ such that $\int \nu_j (\cdot|x) dP(x) = Q_j(\cdot)$ and $$ \int dP (x) \int \frac{dP}{dQ_1} (y)^\beta \frac{dP}{dQ_2} (z)^\beta (1+\beta (1-2\beta))^{f_N(x,y,z)} d\nu_1 (y|x) d\nu_2 (z|x) \le 1 \;, $$ for every $\beta \in (0,1/2)$. Here $f_N$ counts the number of coordinates $k$ for which $x_k \neq y_k$ and $x_k \neq z_k$. In case $Q_1=Q_2$ one may take $\nu_1=\nu_2$. In the special case of $Q_j(\cdot)=P(\cdot|A)$ we recover some of Talagrand's sharper concentration inequalities in product spaces.},
	pages = {no. 9, 83-90},
	issn = {1083-589X},
	doi = {10.1214/ECP.v1-979},    
        url = {http://ecp.ejpecp.org/article/view/979}}