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Spectral comparison on Specht modules and mixing of the interchange process

  • Gil Alon
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Abstract

We characterize the cases in which the minimal eigenvalues of interchange-process Laplacians on two Specht modules can be compared up to a positive multiplicative constant, independent of the edge rates. In the comparable cases, we establish an inverse-polynomial lower bound for this constant. We conjecture that the constant can always be taken to be 2/3. We apply these ideas to the mixing times of the interchange and exclusion processes. Using the comparison method of Hermon, Kozma and Salez, we prove that our conjecture implies a conjecture of Oliveira on the mixing time of the interchange process. We also obtain unconditional mixing-time bounds for both processes.

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Cite

BibTeXRIS
BibTeX
@misc{alon2026spectral,
  title = {{Spectral comparison on Specht modules and mixing of the interchange process}},
  author = {Gil Alon},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22151},
  eprint = {2610.22151},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22151},
}
RIS
TY  - UNPB
TI  - Spectral comparison on Specht modules and mixing of the interchange process
AU  - Gil Alon
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22151
UR  - https://arxiv.org/abs/2610.22151
AB  - We characterize the cases in which the minimal eigenvalues of interchange-process Laplacians on two Specht modules can be compared up to a positive multiplicative constant, independent of the edge rates. In the comparable cases, we establish an inverse-polynomial lower bound for this constant. We conjecture that the constant can always be taken to be 2/3. We apply these ideas to the mixing times of the interchange and exclusion processes. Using the comparison method of Hermon, Kozma and Salez, we prove that our conjecture implies a conjecture of Oliveira on the mixing time of the interchange process. We also obtain unconditional mixing-time bounds for both processes.
ER  -