Timeline for Tail bounds for suprema of random processes
Current License: CC BY-SA 3.0
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| Jun 22, 2015 at 19:13 | comment | added | Roy Han | @oferzeitouni Thanks very much for the correction! It seems to me that log-Sobolev may be well-suited for exponential bound...Is there any positive results that concerning dimension free tail bounds that involve other types of tail scaling, say, polynomially decreasing tail as editted in the question statement? | |
| Jun 22, 2015 at 19:09 | history | edited | Roy Han | CC BY-SA 3.0 |
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| Jun 22, 2015 at 4:40 | comment | added | ofer zeitouni | You are missing a condition on the variance of the $V_i$s. In general, if your $V_i$ satisfy jointly a log-sobolev inequality then the same result will hold. This is the case if for example the joint law of the $V_i$s is of the form $e^{-W(V_1,\ldots,V_n)} d\gamma$ where $\gamma$ is the standard Gaussian and $W$ is convex. What is special about Gaussian is actually the part of the theory that deals with the computation of $EM$. | |
| Jun 22, 2015 at 4:07 | history | edited | Roy Han | CC BY-SA 3.0 |
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| Jun 22, 2015 at 3:56 | history | asked | Roy Han | CC BY-SA 3.0 |