Speaker：Yahong Yang (Pennsylvania State University)

Time：2025-5-23, 15:00

Location：Conference Room C503 at Administration Building at Haiyun Campus 

Abstract:

Choose at random a convex polygon contained in a square and whose vertices have integers coordinates. It has been shown 30 years ago by Barany, Sinai and Vershik that when the square is large, the polygon converges after renormalization to a convex set whose boundary is the union of 4 arcs of parabola which are tangent to the middle of the edges of the square. We study the fluctuations of the polygon away from the limit shape. In particular, we show that these fluctuations are described by a brownian motion with a random drift ant that this drift is a random cubic curve. This is joint work with Théophile Buffière.