Invariant Galton-Watson measures
We introduce a one-parameter family of critical Galton-Watson tree measures invariant under the operation of Horton pruning (cutting tree leaves followed by series reduction). Under a regularity condition, this family of measures are the attractors of critical Galton-Watson trees under consecutive Horton pruning. The invariant Galton-Watson (IGW) measures with i.i.d. exponential edge lengths are the only Galton-Watson measures invariant with respect to all admissible types of generalized dynamical pruning (an operation of erasing a tree from leaves down to the root).
This is a joint work with Ilya Zaliapin (University of Nevada Reno) and Guochen Xu (Oregon State University).