ISOMORPHISMS OF β-DYSON'S BROWNIAN MOTION WITH BROWNIAN LOCAL TIME
Résumé
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 generalizes to β-Dyson's Brownian motion. For β in {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.
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