Geometry of smooth Gaussian fields

Thesis

Gaussian fields are ubiquitous in probability as they are scaling limits of many natural objects, and in applied science as they are instrumental in modelling natural phenomena. In this thesis, we study geometric features of smooth Gaussian fields, like the measure of level sets and the structure of critical points of the field. Large-scale geometry, i.e. studying geometric observables in a domain where the domain size goes to infinity, is of particular interest.

In the first chapter, ...

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Authors: Hegde, AS

• DOI: 10.5287/ora-yjg4p8ywr
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Gaussian fields; critical points
• Subjects: Gaussian processes; Mathematics