Spatial Networks and Probability
主 题: Spatial Networks and Probability
报告人: David Aldous教授 (美国加州大学伯克利分校统计系)
时 间: 2015-05-13 15:00 - 16:00
地 点: 北京国际数学研究中心77201教室（未名湖北岸78号，全斋北边）
The mathematics of large complex networks has been extensively studied over the last 15 years, partly using probability models. The particular setting of networks in two-dimensional space — idealizations of road networks, for instance — is much less studied, and I will talk about several aspects of this setting.
First consider networks linking discrete points (imagine major roads linking large cities). Probabilists are familiar with the “geometric random graph" model and its variants, but there are better “proximity graph” models for connected networks. Now one can ask questions such as:
(a) study properties of such “proximity graph” networks over random points.
(b) what properties — for instance, that route-lengths are linear in Euclidean distance — hold for very general probability models?
(c) if you want to build an “optimal” network, what are the optimization criteria?
(d) what are mathematically natural statistics of a network?
A more technically sophisticated topic is “scale-invariant random networks”, meaning models whose distributions are exactly invariant under Euclidean scaling. This requires working in the continuum plane, so making a precise definition is not trivial. At first sight this is rather abstract mathematics, but it has intriguing connections:
(e) how does your car’s GPS navigation calculate a route quickly?
(f) what are the likely topologies of subnetworks?
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演讲人简介：David Aldous是美国加州大学伯克利分校统计系教授，他于1977年在剑桥大学获博士学位，1979年开始任教于加州大学。他是"Probability Approximations via the Poisson Clumping Heuristic"一书的作者，他与Jim Fill合写的专著"Reversible Markov Chains and Random Walks on Graphs"至今未能定稿却也广为人知。他的概率论研究包括弱收敛，可交换性，马氏链混合时，连续随机树，随机合并，空间随机网络等，贯穿这些问题的中心主题是大规模有限随机结构，当规模趋向无穷时，考察其渐近行为，建立合适的连续随机结构。近期他致力于研究针对现实世界的概率论精确假设。
Aldous教授是英国皇家学会会员和美国国家科学院外籍院士。
