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PreprintarXiv licencearXiv

Uniform many-particle spectral gap inequality and heat kernel bounds for strong attractive interactions

  • S. E. Boutiah
  • D. Kinzebulatov
  • K. R. Madou
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Abstract

We prove a spectral gap inequality for Gaussian measures modified by singular attractive pair interactions. The spectral gap constant is explicit and uniform in the number of particles and the regularization parameter. As an application, we use a corresponding spectral gap inequality for a cutoff interaction weight to obtain two-sided bounds on the transition density of the attractive logarithmic gas.

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Cite

BibTeXRIS
BibTeX
@misc{boutiah2026uniform,
  title = {{Uniform many-particle spectral gap inequality and heat kernel bounds for strong attractive interactions}},
  author = {S. E. Boutiah and D. Kinzebulatov and K. R. Madou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17333},
  eprint = {2609.17333},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17333},
}
RIS
TY  - UNPB
TI  - Uniform many-particle spectral gap inequality and heat kernel bounds for strong attractive interactions
AU  - S. E. Boutiah
AU  - D. Kinzebulatov
AU  - K. R. Madou
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17333
UR  - https://arxiv.org/abs/2609.17333
AB  - We prove a spectral gap inequality for Gaussian measures modified by singular attractive pair interactions. The spectral gap constant is explicit and uniform in the number of particles and the regularization parameter. As an application, we use a corresponding spectral gap inequality for a cutoff interaction weight to obtain two-sided bounds on the transition density of the attractive logarithmic gas.
ER  -