Gaussian Free Fields on the Hypercube

Andrea Collevecchio; Robert Griffiths

doi:10.1007/s10959-025-01403-2

Gaussian Free Fields on the Hypercube

Andrea Collevecchio
, Robert Griffiths

School of Mathematics

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

Abstract

We study a Gaussian free field on the hypercube with covariance function related to the transition kernel of a random walk on the hypercube, killed at a geometric random time. An analysis is made of the asymptotic behaviour of the free field as the dimension of the hypercube tends to infinity. We also obtain a result which connects an Ehrenfest urn with geometric killing to a Pólya urn, which is of independent interest.

Original language	English
Article number	35
Number of pages	14
Journal	Journal of Theoretical Probability
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s10959-025-01403-2
Publication status	Published - Jun 2025

Keywords

Ehrenfest urn
Gaussian free field
Pólya urn
Random walk on a hypercube

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10.1007/s10959-025-01403-2

Cite this

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abstract = "We study a Gaussian free field on the hypercube with covariance function related to the transition kernel of a random walk on the hypercube, killed at a geometric random time. An analysis is made of the asymptotic behaviour of the free field as the dimension of the hypercube tends to infinity. We also obtain a result which connects an Ehrenfest urn with geometric killing to a P{\'o}lya urn, which is of independent interest.",

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N2 - We study a Gaussian free field on the hypercube with covariance function related to the transition kernel of a random walk on the hypercube, killed at a geometric random time. An analysis is made of the asymptotic behaviour of the free field as the dimension of the hypercube tends to infinity. We also obtain a result which connects an Ehrenfest urn with geometric killing to a Pólya urn, which is of independent interest.

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KW - Gaussian free field

KW - Pólya urn

KW - Random walk on a hypercube

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Gaussian Free Fields on the Hypercube

Abstract

Keywords

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Self-Interacting Random Walks

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Gaussian Free Fields on the Hypercube

Abstract

Keywords

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Self-Interacting Random Walks

Cite this