Volume distribution of nodal domains of random band-limited functions

• 成果类型: Article
• 署名作者: Beliaev, Dmitry; Wigman, Igor
• 署名单位: University of Oxford; University of London; King's College London
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0813-x
• 发表日期: 2018
• 页码: 453-492
• 关键词: wave-functions

摘要

We study the volume distribution of nodal domains of families of naturally arising Gaussian random fields on generic manifolds, namely random band-limited functions. It is found that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and continuity of the cumulative probability function, are established.