Abstract
Let μ= μ ω be the branching measure on the boundary ∂ T of a supercritical Galton–Watson tree T = T (ω) . Denote by d(μ,u) and d(μ,u) the lower and upper local dimensions of μ at u∈∂ T . It is well known that almost surely, d(μ,u)= d(μ,u)= logm for μ-almost all u∈∂ T , where m is the expected value of the offspring distribution. Here we find exactly when the result holds for all u∈∂ T , and obtain some limit theorems about the uniform local dimensions of μ. We also find the exact local dimension of μ at u∈∂ T for μ-almost all u.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Annales de l'Institut Henri Poincare / Probabilites et statistiques
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.