ChapterZero

A Rademacher comparison theorem?

Filed under: Mathematics — Alex @ 4:51 pm 6/30/2008

Given Rademacher variables $\epsilon_j$ , what can we say about
$\mathbb{E} \sup_{c > a_j \geq 0} \left|\sum_{i=1}^n \epsilon_j a_j \right|$ versus $\mathbb{E} \sup_{c >a_j \geq 0} \sum_{i=1}^n \epsilon_j a_j$ ?

Anything?

Possibly relevant posts:

The other direction in Khintchine’s inequality for Rademacher sums (9/26/2008)
One direction in Khintchine’s inequality for Rademacher sums (9/26/2008)
Complexification of the Rademacher comparison theorem? (8/18/2008)

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