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2021 Isomorphisms of β-Dyson’s Brownian motion with Brownian local time
Titus Lupu
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Electron. J. Probab. 26: 1-31 (2021). DOI: 10.1214/21-EJP697


We show that the Brydges-Fröhlich-Spencer-Dynkin and the Le Jan’s isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to the β-Dyson’s Brownian motion. For β{1,2,4} this is a consequence of the Gaussian case, however the relation holds for general β. We further raise the question whether there is an analogue of β-Dyson’s Brownian motion on general electrical networks, interpolating and extrapolating the fields of eigenvalues in matrix-valued Gaussian free fields. In the case n=2 we give a simple construction.

Funding Statement

This work was supported by the French National Research Agency (ANR) grant within the project MALIN (ANR-16-CE93-0003).


The author thanks Guillaume Chapuy and Jérémie Bouttier for discussions and references on the beta ensembles. The author thanks Yves Le Jan and Wendelin Werner for their feedback on the preliminary version of the article.


Download Citation

Titus Lupu. "Isomorphisms of β-Dyson’s Brownian motion with Brownian local time." Electron. J. Probab. 26 1 - 31, 2021.


Received: 1 March 2021; Accepted: 1 September 2021; Published: 2021
First available in Project Euclid: 7 October 2021

arXiv: 2009.03026
Digital Object Identifier: 10.1214/21-EJP697

Primary: 15B52, 60B20, 60J55
Secondary: 60G15, 81T18


Vol.26 • 2021
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