The branching number of intermediate growth trees
Year: 2024
Type: article
Abstract: We introduce an “intermediate branching number” (IBN) which captures the branching of intermediate growth trees, similar in spirit to the well-studied branching number of exponential growth trees. We show that the IBN is the critical threshold for several random processes on trees, and analyze the IBN on some examples of interest. Our main result is an algorithm to find spherically symmetric trees with large IBN inside some permutation wreath products. We demonstrate the usefulness of these trees to the study of intermediate growth groups by using them to get the first tight bounds for the firefighter problem on some intermediate growth groups.
Source: Groups Geometry and Dynamics
DOI: 10.4171/ggd/846
Authors: Gideon Amir, Shangjie Yang
Institutions: Bar-Ilan University, Universidade de São Paulo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404995889