Abstract
This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical dimensions. The result is applicable to fractional Brownian sheets and the solutions of systems of stochastic heat and wave equations.
Funding Statement
The research of R.C. Dalang is partially supported by the Swiss National Foundation for Scientific Research, the research of C. Mueller is partially supported by a Simons grant, and Y. Xiao is partially supported by NSF grants DMS-1607089 and DMS-1855185.
Citation
Robert C. Dalang. Cheuk Yin Lee. Carl Mueller. Yimin Xiao. "Multiple points of Gaussian random fields." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP589
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