## The Annals of Probability

### Polarity of points for Gaussian random fields

#### Abstract

We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space–time white noise, or colored noise in spatial dimensions $k\geq1$. Our approach builds on a delicate covering argument developed by M. Talagrand [Ann. Probab. 23 (1995) 767–775; Probab. Theory Related Fields 112 (1998) 545–563] for the study of fractional Brownian motion, and uses a harmonizable representation of the solutions of these stochastic PDEs.

#### Article information

Source
Ann. Probab., Volume 45, Number 6B (2017), 4700-4751.

Dates
Received: May 2015
Revised: November 2016
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1513069271

Digital Object Identifier
doi:10.1214/17-AOP1176

Mathematical Reviews number (MathSciNet)
MR3737922

Zentralblatt MATH identifier
06838131

#### Citation

Dalang, Robert C.; Mueller, Carl; Xiao, Yimin. Polarity of points for Gaussian random fields. Ann. Probab. 45 (2017), no. 6B, 4700--4751. doi:10.1214/17-AOP1176. https://projecteuclid.org/euclid.aop/1513069271

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