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2021 Multiple points of Gaussian random fields
Robert C. Dalang, Cheuk Yin Lee, Carl Mueller, Yimin Xiao
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Electron. J. Probab. 26: 1-25 (2021). DOI: 10.1214/21-EJP589


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.


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Robert C. Dalang. Cheuk Yin Lee. Carl Mueller. Yimin Xiao. "Multiple points of Gaussian random fields." Electron. J. Probab. 26 1 - 25, 2021.


Received: 30 October 2019; Accepted: 30 January 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP589

Primary: 60G15 , 60G17 , 60G60

Keywords: critical dimension , Fractional Brownian sheet , Gaussian random fields , multiple points , Stochastic heat and wave equations


Vol.26 • 2021
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