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 MÃ¶bius 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.