central limit theorem

Benford's law – result of extension of CLT to product of random variables.

Central limit theorem for directional statistics – Central limit theorem applied to the case of directional statistics

Delta method – to compute the limit distribution of a function of a random variable.

Erdős–Kac theorem – connects the number of prime factors of an integer with the normal probability distribution

Fisher–Tippett–Gnedenko theorem – limit theorem for extremum values (such as max{Xn})

Tweedie convergence theorem – a theorem that can be considered to bridge between the central limit theorem and the Poisson convergence theorem