COMPUTER SCIENCE AND DISCRETE MATHEMATICS I | |

Topic: | Super-uniformity of the typical billiard path (proof included) |

Speaker: | Jozsef Beck |

Affiliation: | Rutgers, The State University of New Jersey |

Date: | Monday, October 4 |

Time/Room: | 11:15am - 12:15pm/S-101 |

Video Link: | https://video.ias.edu/csdm/beck |

I will describe the proof of the following surprising result: the typical billiard paths form the family of the most uniformly distributed curves in the unit square. I will justify this vague claim with a precise statement. As a byproduct, we obtain the counter-intuitive fact that the complexity of the test set is almost irrelevant. The error term is shockingly small, and it does not matter that we test uniformity with a nice set (like a circle or a square), or with an arbitrarily ugly Lebesgue measurable subset of the unit square.