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Probabilistic approach to heat kernels of Schrödinger operators with decaying potentials

Xin Chen & Jian Wang

Annals of Applied Probability2026https://doi.org/10.1214/25-aap2209article
ABDC A
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0.50

Abstract

We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator −12Δ+V on Rd, where the potential V(x) is locally bounded and behaves like c|x|−α near infinity with α∈(0,2) and c>0, or with α>0 and c<0. Our results improve all known results in the literature, and it seems that the current paper is the first one where two-sided matching heat kernel bounds for the long range potentials are established. The results of the paper mostly rely on probabilistic approaches.

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https://doi.org/https://doi.org/10.1214/25-aap2209

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@article{xin2026,
  title        = {{Probabilistic approach to heat kernels of Schrödinger operators with decaying potentials}},
  author       = {Xin Chen & Jian Wang},
  journal      = {Annals of Applied Probability},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aap2209},
}

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Probabilistic approach to heat kernels of Schrödinger operators with decaying potentials

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