Self-Similar Markov Trees and Scaling Limits

Self-similar Markov trees form a remarkable family of random compact real trees equipped with a decoration function that is positive on the skeleton, encompassing the Brownian continuum random tree, stable Lévy trees, fragmentation trees, and growth-fragmentation trees. In this book, the authors develop a consistent and unified theory of self-similar Markov trees by bringing together and vastly generalizing results that had been scattered across the random tree literature over several decades. They begin with in-depth coverage of the construction of self-similar Markov trees, then address the study of self-similar Markov trees in the continuous. In Part II, the authors build on this material and introduce readers to current research. They establish general invariance principles for Galton-Watson trees with integer types and illustrate them through numerous combinatorial classes of random trees that have appeared in the literature.