【学术报告】On the number of level sets of smooth Gaussian fields

• 主讲人：Dmitry Belyaev
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium by Sino-Russian Mathematics Center
• 时间： 2022-03-08 21:00 - 2022-03-08 22:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/EDA3BDF8D06B8765C1542BE7278C7D3B
Valid Until: 2026-06-30 23:59

 

Abstract: The number of zeroes or, more generally, level crossings of a Gaussian process is a classical subject that goes back to the works of Kac and Rice who studied zeroes of random polynomials.  The number of zeroes or level crossings has two natural generalizations in higher dimensions. One can either look at the size of the level set or the number of connected components. The surface area of a level set could be computed in a similar way using Kac-Rice formulas. On the other hand, the number of the connected components is a `non-local' quantity which is notoriously hard to work with. The law of large numbers has been established by Nazarov and Sodin about ten years ago. In this talk, we will briefly discuss their work and then discuss the recent progress in estimating the variance and deriving the central limit theorem. The talk is based on joint work with M. McAuley and S. Muirhead. 

 

Bio: Dmitry Belyaev is a Professor of Mathematics and Tutorial Fellow at St . Anne’s College. Before coming to Oxford in 2011 he was an Assistant Professor at Princeton University (2008-2011) and Veblen Research Instructor at Princeton University and IAS (2005-2008). He received PhD in 2005 from the Royal Institute of Technology in Stockholm and B.Sc/M.Sc from St. Petersburg State University.
His main research interests are on the interface between analysis and probability including (but not limited to) Geometry of Gaussian fields, Growth models, Geometric function theory, Schramm-Loewner Evolution and critical lattice models.