Transportation Approach to Some Concentration Inequalities in Product Spaces
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Transportation Approach to Some Concentration Inequalities in Product Spaces |
| 2. | Creator | Author's name, affiliation, country | Amir Dembo; Stanford University |
| 2. | Creator | Author's name, affiliation, country | Ofer Zeitouni; Technion - Israel Institute of Technology |
| 3. | Subject | Discipline(s) | Mathematics |
| 3. | Subject | Keyword(s) | Concentration inequalities, product spaces, transportation. |
| 3. | Subject | Subject classification | 60E15,28A35. |
| 4. | Description | 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. |
| 5. | Publisher | Organizing agency, location | |
| 6. | Contributor | Sponsor(s) | |
| 7. | Date | (YYYY-MM-DD) | 1996-10-24 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Uniform Resource Identifier | http://ecp.ejpecp.org/article/view/979 |
| 10. | Identifier | Digital Object Identifier | 10.1214/ECP.v1-979 |
| 11. | Source | Journal/conference title; vol., no. (year) | Electronic Communications in Probability; Vol 1 |
| 12. | Language | English=en | en |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
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