# What is the difference between a non-central limit theorem and the usual central limit theorems?

I'm reading a paper where the authors prove the following theorem.

They then say that this constitutes a non-central limit theorem for the variables in question. Since I have never heard this term (but I am a little comfortable with the concept of central limit theorems), I am having trouble understanding what they mean by it. Does it mean that the limiting variable does not have a mean equal to zero?

• You need to define some terms to make this answerable ... – kjetil b halvorsen Apr 13 at 4:26