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I would like to calculate or at least to estimate some expectation.

Let $r_k$, $k=1,\ldots, 2n$ be random variables with $P(r_k=1)=P(r_k=-1)=\frac 12$ and such that half of them $r_k=1$ and half $r_k=-1$. Let $b_k$, $k=1,\ldots, 2n$ be real numbers.

I would like to calculate $ E\left(\prod_{i=1}^n\prod_{j=n+1}^{2n} \exp(r_ib_ir_jb_j)\right). $

Any ideas would be very helpful.

Thank you.

  • 0
    Sorry, could you please elaborate your answer. I am not familiar with decoupling...2012-02-23

0 Answers 0