The Local Limit Theorem: A Historical Perspective

The local limit theorem describes how the density of a sum of random variables follows the normal curve. however the local limit theorem is often seen as a curiosity of no particular importance when compared with the central limit theorem. nevertheless the local limit theorem came first and is in fact associated with the foundation of probability theory by blaise pascal and pierre de fermat and was originally formalized by jakob bernoulli, abraham demoivre and pierre-simon laplace.here we describe the historical roots of the local limit theorem.we describe how it was supplanted by the central limit theorem inapplications. then we review the revival started by b. v. gnedenkoand we describe modern developments.