主 题: Percolation on Euclidean and Non-Euclidean Graphs.
报告人: Prof.Chris Wu ((Penn State University))
时 间: 0000-00-00
地 点: 理科一号楼1418
摘要: Percolation theory can be regarded as a random graph theory. It was originally introduced as a probabilistic model of studying flow through a discrete random system, such as particles flowing through the filter of a gas mask. It has a wide range of applications in networks, materials science, chemistry, and statistical physics. Percolation on an infinite graph G can be described as follows: Color an edge of G red (respectively, white) with probability p (respectively, 1-p). Do this to all edges independently to each other.
>If G is the Euclidean lattice $Z^d$ (where d>1), then it is a fundamental result that the random red sub-graphs undergo a phase transition. More precisely, there exists a critical value $p_c$ such that when $p < p_c$ all red connected components are finite, while when $p > p_c$ there is a unique infinite red connected component. An important (but still open in many cases) question is: what happens at $p = p_c$?
>In the case where G is a non-Euclidean graph, the percolation model exhibits quite different phenomenon. For example, in this case the model may have multiple phase transitions. In this talk we will review several fundamental results of the model on both Euclidean and non-Euclidean graphs and introduce one new.