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PreprintCC BY 4.0arXiv

Heat Kernel Estimates for Random Walks with Killing on Transient Graphs

  • Emily Dautenhahn
  • Anthony Graves-McCleary
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Abstract

We give matching two-sided estimates for heat kernels obtained from Schrödinger operators Δ+W on weighted graphs. The graphs we consider are transient and admit two-sided sub-Gaussian heat kernel estimates for the Laplacian Δ, and the potentials W decay to zero at infinity. We offer two proofs for one of our main results: one using the Feynman-Kac formula, and one without using it. Our results apply to fractal-type graphs such as graphical Sierpinski carpets, among other examples.

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Cite

BibTeXRIS
BibTeX
@misc{dautenhahn2026heat,
  title = {{Heat Kernel Estimates for Random Walks with Killing on Transient Graphs}},
  author = {Emily Dautenhahn and Anthony Graves-McCleary},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19285},
  eprint = {2610.19285},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19285},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Heat Kernel Estimates for Random Walks with Killing on Transient Graphs
AU  - Emily Dautenhahn
AU  - Anthony Graves-McCleary
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19285
UR  - https://arxiv.org/abs/2610.19285
AB  - We give matching two-sided estimates for heat kernels obtained from Schrödinger operators Δ+W on weighted graphs. The graphs we consider are transient and admit two-sided sub-Gaussian heat kernel estimates for the Laplacian Δ, and the potentials W decay to zero at infinity. We offer two proofs for one of our main results: one using the Feynman-Kac formula, and one without using it. Our results apply to fractal-type graphs such as graphical Sierpinski carpets, among other examples.
ER  -