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Please help me with this question. It is simple, but I am confused right now.

For $i=1,...,n$, $\alpha_i \in C$ and $r_i$ independent and is such that $P(r_i=1)=1-P(r_i=-1)$.

I know that $E|\sum_{i=1}^n\alpha_i r_i|^p\leq C \sqrt p \| \alpha \|_2$.

I need to bound $E|\sum_{i=1}^{n-1}(\alpha_i-1) r_i|^p$.

Thank you

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    In other words, an upper bound linear in $\|\alpha\|_2$ is impossible so you are trying a **smaller** upper bound? Not sure there is much hope... :-) (Unrelated: please use the @ thing if you want the people you are talking to, to see your comments, I stumbled upon yours by chance.)2012-03-12

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