Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics

We compute the resultant measures for the iterations Pj, j≥1, of a polynomial P of degree >1 on the nth level Trucco trees Γn, n≥0, in the Berkovich projective line over a non-archimedean field and also determine their barycenters. As applications, we study the asymptotic of those barycenters as n→∞, and establish a uniform stationarity of Rumely’s minimal resultant loci of Pj or equivalently that of the potential semistable reduction loci of Pj as j→∞. We also establish several equidistribution results for the resultant measures themselves as n→∞.