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Journal Articles Electronic Journal of Probability Year : 2021

Isomorphisms of β-Dyson’s Brownian motion with Brownian local time

Abstract

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 P t1, 2, 4u 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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Dates and versions

hal-03405268 , version 1 (27-10-2021)

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Cite

Titus Lupu. Isomorphisms of β-Dyson’s Brownian motion with Brownian local time. Electronic Journal of Probability, 2021, 26 (none), ⟨10.1214/21-ejp697⟩. ⟨hal-03405268⟩
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