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Large deviations for the CRT
Abstract
We establish large deviation principles both for the CRT in the Gromov-Hausdorff topology and for the CRT weighted by its mass measure in the Gromov-Hausdorff-Prohorov topology. In the first case, the rate function of a tree 𝒯 is half the square of the length of 𝒯. In the second case, the rate function of a pair (𝒯,μ) is half the integral with respect to the length measure of 𝒯 of the inverse of the absolutely continuous part of μ.
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BibTeX
@misc{gall2026large,
title = {{Large deviations for the CRT}},
author = {Jean-François Le Gall},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12807},
eprint = {2609.12807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12807},
}
RIS
TY - UNPB
TI - Large deviations for the CRT
AU - Jean-François Le Gall
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12807
UR - https://arxiv.org/abs/2609.12807
AB - We establish large deviation principles both for the CRT in the Gromov-Hausdorff topology and for the CRT weighted by its mass measure in the Gromov-Hausdorff-Prohorov topology. In the first case, the rate function of a tree 𝒯 is half the square of the length of 𝒯. In the second case, the rate function of a pair (𝒯,μ) is half the integral with respect to the length measure of 𝒯 of the inverse of the absolutely continuous part of μ.
ER -