On the GFF with one free boundary condition

Yong Han, Yuefei Wang and Zipeng Wang

Statistics & Probability Letters, 2023, vol. 193, issue C

Abstract: In this note, we shall obtain 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. Our proof of the main result relies on both the martingale methods, and finding out the explicit form of the solution of the partial differential equation derived from the Ito’s calculus with extra efforts.

Keywords: SLEκ; Level line of GFF; Mixed boundary conditions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109699

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