Timeline for Upper-bound of the tail of a weighted sum of iid random variables

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Feb 29 at 19:13	comment	added	ofer zeitouni		You don't need that, since the entries of large a_i contribute order 1, while the t you care about is proportional to sqrt{n}; also since you care only for probability close to 1, you can a-priori only consider $k=n/2+O(\sqrt{n})$.
Feb 29 at 12:53	comment	added	odile		Thank you very much for your answer. From what I understand, I can make some statistics on the $\lVert a \rVert_B$ (the norm of the surviving indices) in order to refine the bound $\lVert a \rVert_B$ < 1 in my formula. If the cardinal of B is k, then I have mean($\lVert a \rVert_B$) = $\sqrt{k/n}$ and var($\lVert a \rVert_B$) $\le$ $k(n-k)/n^2$ if I am not mistaken. But I need to have some bound on the proportion of $\lVert a \rVert_B$ lower than say $\epsilon$. How do I get to that?
Feb 28 at 21:07	history	edited	ofer zeitouni	CC BY-SA 4.0	deleted 3 characters in body
Feb 28 at 16:48	history	edited	ofer zeitouni	CC BY-SA 4.0	Corrected some typos
Feb 28 at 15:17	history	edited	ofer zeitouni	CC BY-SA 4.0	added 32 characters in body
Feb 27 at 20:01	history	answered	ofer zeitouni	CC BY-SA 4.0