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.
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.
"Multiple points of Gaussian random fields." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP589