Limit Theorems for the M\"{o}bius Function and Statistical Mechanics

SPECIAL LECTURE
Topic:Limit Theorems for the M\"{o}bius Function and Statistical Mechanics
Speaker:Francesco Cellarosi
Affiliation:Princeton University
Date:Tuesday, March 29
Time/Room:4:00pm - 5:00pm/S-101

I will present a recent joint work with Ya.G. Sinai. We investigate the ``randomness" of the classical Möbius function by means of a statistical mechanical model for square-free numbers and we prove some new results, including a non-standard limit theorem where the Dickman-De Bruijn distribution appears. Although we use a probabilistic approach, this work is inspired by a conjecture by P. Sarnak, and by a number of recent results relating Number Theory and Ergodic Theory.