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Hypocoercivity of Tempered Bouncy Particle Samplers for Heavy-Tailed Targets

  • Aleksandar Mijatović
  • Vinayak Niraj
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Abstract

We introduce the Tempered Bouncy Particle Sampler, a state-dependently tempered generalisation of the Bouncy Particle Sampler. Adapting the hypocoercivity framework of Dolbeault, Mouhot and Schmeiser (2010), we establish explicit, non-asymptotic exponential convergence bounds for a broad class of heavy-tailed targets that need not be log-concave or radially symmetric, including distributions with polynomial tails. The convergence rate is linked to the spectral gap of a tempered Langevin diffusion with the same invariant distribution, making a weighted Poincaré inequality the key assumption. We give admissible tempering choices for polynomial and stretched-exponential tails and derive mixing-time bounds with polynomial dependence on the dimension.

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Cite

BibTeXRIS
BibTeX
@misc{mijatovic2026hypocoercivity,
  title = {{Hypocoercivity of Tempered Bouncy Particle Samplers for Heavy-Tailed Targets}},
  author = {Aleksandar Mijatović and Vinayak Niraj},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.29657},
  eprint = {2608.29657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29657},
}
RIS
TY  - UNPB
TI  - Hypocoercivity of Tempered Bouncy Particle Samplers for Heavy-Tailed Targets
AU  - Aleksandar Mijatović
AU  - Vinayak Niraj
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2608.29657
UR  - https://arxiv.org/abs/2608.29657
AB  - We introduce the Tempered Bouncy Particle Sampler, a state-dependently tempered generalisation of the Bouncy Particle Sampler. Adapting the hypocoercivity framework of Dolbeault, Mouhot and Schmeiser (2010), we establish explicit, non-asymptotic exponential convergence bounds for a broad class of heavy-tailed targets that need not be log-concave or radially symmetric, including distributions with polynomial tails. The convergence rate is linked to the spectral gap of a tempered Langevin diffusion with the same invariant distribution, making a weighted Poincaré inequality the key assumption. We give admissible tempering choices for polynomial and stretched-exponential tails and derive mixing-time bounds with polynomial dependence on the dimension.
ER  -