Gaussian Free Fields on the Hypercube

Andrea Collevecchio () and Robert Griffiths ()
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Andrea Collevecchio: Monash University
Robert Griffiths: Monash University

Journal of Theoretical Probability, 2025, vol. 38, issue 2, 1-14

Abstract: 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.

Keywords: Ehrenfest urn; Gaussian free field; Pólya urn; Random walk on a hypercube (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01403-2

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