Abstract
We study vector-valued solutions to systems of nonlinear stochastic heat equations with multiplicative noise,
Here, , and is an -valued space–time white noise. We say that a point is polar if
We show that, in the critical dimension , almost all points in are polar.
Funding Statement
The first author was supported in part by the Swiss National Foundation for Scientific Research.
The second author was supported in part by a Simons Collaboration Grant.
The third author was supported in part by NSF Grants DMS-1607089 and DMS-1855185.
Acknowledgments
The research reported in this paper was initiated at the Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne, Switzerland, during the semester program “Stochastic Analysis and Applications” in Spring 2012. We thank this institution for its hospitality and support.
Citation
Robert C. Dalang. Carl Mueller. Yimin Xiao. "Polarity of almost all points for systems of nonlinear stochastic heat equations in the critical dimension." Ann. Probab. 49 (5) 2573 - 2598, September 2021. https://doi.org/10.1214/21-AOP1516
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