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Very high genus double Hurwitz numbers via mixing times
Abstract
We obtain very high genus asymptotics for double Hurwitz numbers when both the size n and the genus g go to infinity, under the constraint that g grows much faster than n, more precisely that 2g/n−ln n→∞. Our proof relies on adapting arguments about the mixing time of the transposition random walk introduced by Diaconis and Shahshahani.
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BibTeX
@misc{louf2026very,
title = {{Very high genus double Hurwitz numbers via mixing times}},
author = {Baptiste Louf and Lucas Teyssier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16818},
eprint = {2610.16818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16818},
}
RIS
TY - UNPB
TI - Very high genus double Hurwitz numbers via mixing times
AU - Baptiste Louf
AU - Lucas Teyssier
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16818
UR - https://arxiv.org/abs/2610.16818
AB - We obtain very high genus asymptotics for double Hurwitz numbers when both the size n and the genus g go to infinity, under the constraint that g grows much faster than n, more precisely that 2g/n−ln n→∞. Our proof relies on adapting arguments about the mixing time of the transposition random walk introduced by Diaconis and Shahshahani.
ER -