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Fractal percolation and its connectivity properties (1)

发布日期:2024-04-11点击数:

报告人:Henk Don(荷兰Nijmegen大学)

时间:2024年04月15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 AlgorithmsBernoulliJournal of Number TheoryActa ArithmeticaJournal of Statistical Physics期刊发布多篇论文。


邀请人:数学研究中心


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