Work

(Random) Trees of Intermediate Volume Growth

Year: 2025

Type: article

Abstract: ABSTRACT For every function that grows at least linearly and at most exponentially, if it is sufficiently well‐behaved, we can construct a tree of uniform volume growth , or more precisely, for constants that only depend on . Here denotes the ball of radius centered at a vertex . In particular, this yields examples of trees of uniform intermediate (i.e., super‐polynomial and sub‐exponential) growth. We use this construction to provide the first examples of unimodular random rooted trees of uniform intermediate growth, answering a question by Itai Benjamini. We find a peculiar change in structural properties for these trees at growth . Our results can be applied to obtain triangulations of for with various uniform growth behaviors, as well as Riemannian metrics on for the same wide range of growth behaviors.

Source: Random Structures and Algorithms

DOI: 10.1002/rsa.70035

Authors: George Kontogeorgiou, Martin Winter

Institutions: Center for Mathematical Modeling, University of Chile, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,550

Funder: Engineering and Physical Sciences Research Council