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## One direction in Khintchine’s inequality for Rademacher sums

The Khintchine inequality for Rademacher sums says that given a real vector the -th moment of the random sum is equivalent to the length of : where are constants which depend on. Here the expectation is taken w.r.t to the, which are i.i.d Bernoulli r.v.s — i.e. Rademacher r.v.s Today I’ll [...]

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### The Sum of Subspaces

Academics / Mathematics : The Unapologetic Mathematician (5 years ago)

We know what the direct sum of two vector spaces is. That we define abstractly and without reference to the internal structure of each space. It’s sort of like the disjoint union of sets, and in fact the basis for a direct sum is th... Read Post

### 254A, Notes 2: The central limit theorem

Academics / Mathematics : Terence Tao's Blog (3 years ago)

Consider the sum of iid real random variables of finite mean and variance for some. Then the sum has mean and variance, and so (by Chebyshev’s inequality) we expect to usually have size. To put it another way, if we consider the nor... Read Post

### The other direction in Khintchine’s inequality for Rademacher sums

Academics / Mathematics : Chapter Zero (5 years ago)

It turns out to be just an application of Jensen’s inequality: The last equality holds because of the independence of the Rademacher variables. Read Post