A note on the GFF with one free boundary condition
Yong Han, Yuefei Wang, Zipeng Wang
TL;DR
This paper derives an explicit probability formula for the level line of the Gaussian Free Field with mixed boundary conditions, extending previous results from Dirichlet cases.
Contribution
It provides a new explicit formula for GFF level lines with mixed boundary conditions, broadening understanding of boundary effects in GFF models.
Findings
Explicit probability formula for GFF level lines with mixed boundary conditions
Generalization of previous Dirichlet boundary results
Enhanced understanding of boundary influence on GFF level lines
Abstract
In this note, we shall prove an explicit formula on the probability of the level line of the Gaussian Free Field (GFF) with mixed boundary condition terminating at the free boundary, which generalizes the results of GFF with Dirichlet boundary condition.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Geometry and complex manifolds