Central Limit Theorem, or CLT, is a statistical theory stating that as the size of a sample grows, the results tend to approximate a normal distribution of results. Read more here.

The central limit theorem for ergodic stationary processes obtained by Gordin is shown to hold for general stationary processes. In this case, the limit law is a mixture of normals.

A classical generalized central limit theorem is recovered as a special case, provided a mild but natural additional condition holds. Our approach contrasts with previous arguments for the result in ...