Compactness and fractal dimensions of inhomogeneous continuum random trees

Abstract

We introduce a new stick-breaking construction for inhomogeneous continuum random trees (ICRT). This new construction allows us to prove the necessary and sufficient condition for compactness conjectured by Aldous, Miermont and Pitman arXiv:math/0401115 by comparison with L\'evy trees. We also compute the fractal dimensions (Minkowski, Packing, Hausdorff).