Proof of `Exponential concentration on finite product spaces` (1st statement)
groundedproofs/Lax253009Proofs/ExponentialBounds.lean · lax-253009
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Convexity bounds the exponential by its chord between -u and u. The mean zero assumption cancels the linear part, leaving cosh(u) ≤ exp(u²/2).