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Article Dans Une Revue Electronic Journal of Probability Année : 2021

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 the 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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Dates et versions

hal-02996476 , version 1 (09-11-2020)
hal-02996476 , version 2 (07-10-2021)

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Titus Lupu. ISOMORPHISMS OF β-DYSON'S BROWNIAN MOTION WITH BROWNIAN LOCAL TIME. Electronic Journal of Probability, 2021, 26, pp.1-31. ⟨10.1214/21-EJP697⟩. ⟨hal-02996476v2⟩
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