Ballot Theorems for the Two-Dimensional Discrete Gaussian Free Field

Stephan Gufler; Oren Louidor

doi:https://doi.org/10.1007/s10955-022-02970-y

Ballot Theorems for the Two-Dimensional Discrete Gaussian Free Field

Stephan Gufler, Oren Louidor

Data and Decision Sciences

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We provide uniform bounds and asymptotics for the probability that a two-dimensional discrete Gaussian free field on an annulus-like domain and with Dirichlet boundary conditions, stays negative as the ratio of the radii of the outer and the inner boundary tends to infinity. Such estimates are often needed in the study of extreme values of the discrete Gaussian free field on planar domains.

Original language	English
Article number	13
Journal	Journal of Statistical Physics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1007/s10955-022-02970-y
State	Published - Oct 2022

Keywords

Ballot theorems
Extreme value theory
Gaussian free field
Log correlated fields

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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https://doi.org/10.1007/s10955-022-02970-y

Cite this

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title = "Ballot Theorems for the Two-Dimensional Discrete Gaussian Free Field",

abstract = "We provide uniform bounds and asymptotics for the probability that a two-dimensional discrete Gaussian free field on an annulus-like domain and with Dirichlet boundary conditions, stays negative as the ratio of the radii of the outer and the inner boundary tends to infinity. Such estimates are often needed in the study of extreme values of the discrete Gaussian free field on planar domains.",

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AB - We provide uniform bounds and asymptotics for the probability that a two-dimensional discrete Gaussian free field on an annulus-like domain and with Dirichlet boundary conditions, stays negative as the ratio of the radii of the outer and the inner boundary tends to infinity. Such estimates are often needed in the study of extreme values of the discrete Gaussian free field on planar domains.

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KW - Extreme value theory

KW - Gaussian free field

KW - Log correlated fields

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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Ballot Theorems for the Two-Dimensional Discrete Gaussian Free Field

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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