PreprintarXiv licencearXiv
On self-similar random quotients of the line
Abstract
A surprisingly wide variety of important random fractal metric spaces in modern probability theory can be viewed as self-similar random quotients of the real line, including the continuum random tree, Liouville quantum gravity surfaces, the trace of Brownian motion in ℝd, and self-similar (s=2d) long-range percolation on ℝ. We prove that the metric and resistance growth dimensions are well-defined in a certain sense for every random metric space in a class containing all of the above examples. Our results are new for the trace of Brownian motion.
Related
- The Exact Overlaps Conjecture for Self-Similar Measures on the Real Line
- Random self-similar series on the two-dimensional torus
- Khintchine dichotomy for images of self-similar measures and almost random walks
- Dimension properties of a family of random self-similar iterated function systems
- Coding multiplicity in self-similar sets on the line
BibTeX
@misc{baumler2026selfsimilar,
title = {{On self-similar random quotients of the line}},
author = {Johannes Bäumler and Tom Hutchcroft},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39953},
eprint = {2610.39953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39953},
}
RIS
TY - UNPB
TI - On self-similar random quotients of the line
AU - Johannes Bäumler
AU - Tom Hutchcroft
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39953
UR - https://arxiv.org/abs/2610.39953
AB - A surprisingly wide variety of important random fractal metric spaces in modern probability theory can be viewed as self-similar random quotients of the real line, including the continuum random tree, Liouville quantum gravity surfaces, the trace of Brownian motion in ℝ^d, and self-similar (s=2d) long-range percolation on ℝ. We prove that the metric and resistance growth dimensions are well-defined in a certain sense for every random metric space in a class containing all of the above examples. Our results are new for the trace of Brownian motion.
ER -