Short Talk: Mie Glückstad

Duquesne and Le Gall (2002) established an invariance principle for Galton-Watson trees, characterizing the scaling limits of discrete Galton-Watson trees as a class of continuum random trees. This invariance principle, however, relied on two assumptions: 1) that the Galton-Watson trees are subcritical, and 2) that Grey’s condition is satisfied in the limit. The invariance principle has since been extended in work by Duquesne and Winkel (2019, 2025+) leaving open only the case where both assumptions 1) and 2) fail. To deal with the case where 1) holds and 2) fails, Duquesne and Winkel (2025+) introduce a notion of mass erasure, which is a technique reminiscent to that of leaf-length erasure or trimming, as known from e.g. Neveu (1986). To address the final case where both 1) and 2) fail, we extend the notion of mass erasure from finitely measured R-trees to R-trees equipped with boundedly finite measures and discuss suitable notions of convergence in this setting.