Limit theorems for random normalized distortion (Q1431553)

This paper is devoted to the study of the asymptotics of the distortion when the codes are random, drawn from a sequence of independent and identically distributed random variables. The author presents a weak law of large numbers, a strong law of large numbers and, in the one-dimensional setting, a central limit theorem. He also shows that the random distortion and the optimal distortion vanish almost surely at the same rate.