The Gaussian free field and Hadamard's variational formula
Haakan Hedenmalm, Pekka J. Nieminen
TL;DR
This paper explores the relationship between the Gaussian free field on planar domains and Hadamard's variational formula, providing a new integral operator perspective on domain perturbations affecting the Green function.
Contribution
It introduces a novel integral operator linking the Gaussian free field to Hadamard's formula, enhancing understanding of Green function variations under domain changes.
Findings
Established a connection between Gaussian free field and Hadamard's variational formula
Developed a natural integral operator related to domain perturbations
Provided insights into Green function behavior under domain changes
Abstract
We relate the Gaussian free field on a planar domain to the variational formula of Hadamard which explains the change of the Green function under a perturbation of the domain. This is accomplished by means of a natural integral operator related to Hadamard's formula.
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Taxonomy
TopicsMatrix Theory and Algorithms · Mathematics and Applications · Mathematical functions and polynomials