报告人：Henk Don（荷兰Nijmegen大学）

时间：2024年04月22日 09：30-

地点：理科楼LA103

摘要：Fractal percolation is a stochastic model for porous media, introduced in 1974 by Mandelbrot. One can see it as a random subset of the unit square, obtained by randomly removing smaller squares. Since the removed squares get smaller and smaller, the limiting set will have a fractal structure. Depending on the parameters, the properties of the limiting set greatly vary. In particular, there is a sharp phase transition where the limiting set changes from very disconnected to very connected. This involves a critical parameter value $p_c$.

In these talks I will introduce and discuss the model. We will explore the connectivity properties and discuss how to formalize and prove them. Further, we will discuss methods to find rigorous bounds for $p_c$.

简介：Henk Don博士毕业于荷兰代尔夫特理工大学，现为荷兰Nijmegen大学助理教授。研究方向：概率论。其中包括随机分形、随机图、渗流、分支过程、概率组合等。在Random Structures and Algorithms、Bernoulli、Journal of Number Theory、Acta Arithmetica、Journal of Statistical Physics等期刊发布多篇论文。

邀请人：数学研究中心

欢迎广大师生积极参与！