Electronic Communications in Probability

Weighted graphs and complex Gaussian free fields

Gregory F. Lawler and Petr Panov

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We prove a combinatorial statement about the distribution of directed currents in a complex “loop soup” and use it to give a new proof of the isomorphism, which relates loop measures and complex Gaussian free fields.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 38, 9 pp.

Received: 7 June 2018
Accepted: 2 April 2019
First available in Project Euclid: 22 June 2019

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Primary: 60J05: Discrete-time Markov processes on general state spaces

Gaussian free field random walk loop soup isomorphism theorem

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Lawler, Gregory F.; Panov, Petr. Weighted graphs and complex Gaussian free fields. Electron. Commun. Probab. 24 (2019), paper no. 38, 9 pp. doi:10.1214/19-ECP225. https://projecteuclid.org/euclid.ecp/1561169054

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