Cramér's theorem (large deviations)

Cramér's theorem is a fundamental result in the field of large deviations theory, which examines the asymptotic behavior of the probabilities of rare events. Specifically, Cramér's theorem provides a way to quantify the likelihood of deviations of a sum of independent random variables from its expected value. The theorem states that if we have a sequence of independent and identically distributed (i.i.d.