Also, for a very brief (but excellent!) introduction, see:
http://algo.inria.fr/seminars/sem96-97/deshouillers.pdf

Baez-Duarte, wrote a beautiful article, giving us a "probabilistic" derivation of the Hardy-Ramanujan asymptotic for p(n). He's essentially interpreting "probabilistically" the saddle-point method, and this type of thinking was central to me for a long time.

The exact reference for his paper is: MR1427803 (98b:60036) Báez-Duarte, Luis Hardy-Ramanujan's asymptotic formula for partitions and the central limit theorem. Adv. Math. 125 (1997), no. 1, 114--120

It's online, but I can't post more than one link... :-(

Finally, I recommend visiting the home-pages of Kevin Ford and Gerald Tenenbaum...