Intrinsic complexity and its scaling law: from approximation of random vectors and random fields to high frequency waves

浙江大学数学科学学院九十周年院庆系列活动之六十六 

求是前沿讲座

Intrinsic complexity and its scaling law: from approximation of randomvectors and random fields to high frequency waves

报告人：Hongkai Zhao教授

University of California, Irvine

时间:  2018年8月13日（星期一）下午3:00开始

地点: 浙江大学玉泉校区逸夫工商管理楼200-9

摘要：

Wecharacterize the intrinsic complexity of a set in a metric space by the leastdimension of a linear space that can approximate the set to a given tolerance.This is dual to the characterization using Kolmogorov n-width, the distancefrom the set to the best n-dimensional linear space. We start with approximateembedding of a set of random vectors (principal component analysis a.k.a.singular value decomposition), then study the approximation of random fieldsand high frequency waves. We provide lower bounds and upper bounds for theintrinsic complexity and its explicit asymptotic scaling laws in terms of thetotal number of random vectors, the correlation length for random fields, andthe wave length for high frequency waves respectively.