Fluctuations of random lattice polygons

：Philippe MARCHAL（法国国家科学研究中心、巴黎第十三大学）
：2025-05-23 15:00
：海韵园行政楼C503

报告人：Philippe MARCHAL（法国国家科学研究中心、巴黎第十三大学）

时  间：2025年5月23日15:00

地  点：海韵园行政楼C503

内容摘要:

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.

个人简介：

Professor Marchal studied at the École Normale Supérieure and graduated with a PhD in mathematics from the Sorbonne Universsit in 1999. He obtained the “Habilitation à diriger des recherches” from the Sorbonne University in 2010. Since the year 2000, he is a researcher with the CNRS, now working at the Université Paris 13. His scientific interests lie in probability, specifically Lévy processes, random trees, and random generation.

 

联系人：宋翀