 Rademacher large-deviation rate function

ID: rademacher-large-deviation-rate-function

For a uniform random sign

X \in {- 1, 1}

ψ (λ) = lo g cosh λ

and

ψ^{*} (x) = \frac{( 1 + x ) l o g ( 1 + x ) + ( 1 - x ) l o g ( 1 - x )}{2}

for

∣ x ∣ \leq 1

, with value

+ \infty

outside that interval.

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