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

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