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

We show that the Brydges-Frohlich-Spencer-Dynkin and the Le Jan's isomorphisms between the Gaussian free fields and the occupation times of symmetric Markov processes generalize to the 0-Dyson's Brownian motion. For 0 P t1, 2, 4u this is a consequence of the Gaussian case, however the relation holds for general 0. We further raise the question whether there is an analogue of 0-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.