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Main Author: Derrien, Jean-Marc
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.06020
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author Derrien, Jean-Marc
author_facet Derrien, Jean-Marc
contents The gaussian free field on the unit disk $D$ can be seen as a two-dimensional version of the Brownian bridge on the interval [0,1]. It is intrinsically associated with the Sobolev space $H_0^1 (D)$. To define the latter, we can choose any metric conformally equivalent to the Euclidean metric on $D$. This note is an introduction to the gaussian free field on the unit disk whose aim is to highlight some of the conveniences offered by hyperbolic geometryon $D$ to describe the first properties of this probabilistic object.
format Preprint
id arxiv_https___arxiv_org_abs_2501_06020
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Averaging over the circles the gaussian free field in the Poincar{é} disk
Derrien, Jean-Marc
Probability
The gaussian free field on the unit disk $D$ can be seen as a two-dimensional version of the Brownian bridge on the interval [0,1]. It is intrinsically associated with the Sobolev space $H_0^1 (D)$. To define the latter, we can choose any metric conformally equivalent to the Euclidean metric on $D$. This note is an introduction to the gaussian free field on the unit disk whose aim is to highlight some of the conveniences offered by hyperbolic geometryon $D$ to describe the first properties of this probabilistic object.
title Averaging over the circles the gaussian free field in the Poincar{é} disk
topic Probability
url https://arxiv.org/abs/2501.06020