|COMPUTER SCIENCE AND DISCRETE MATHEMATICS I|
|Topic:||Super-uniformity of the typical billiard path (proof included)|
|Affiliation:||Rutgers, The State University of New Jersey|
|Date:||Monday, October 4|
|Time/Room:||11:15am - 12:15pm/S-101|
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.