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PreprintCC BY-NC-ND 4.0arXiv

Exponential decay of fractional moments in the H2|2 model on ℤ2

  • Jinglin Wang
  • Xiaolin Zeng
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Abstract

For the H2|2 model on ℤ2, we show that, at energy zero, the fractional moments of Green functions, 𝔼[ G(x,y)s] decay exponentially in the distance between x and y, for every constant edge weight W>0 and every 0<s<1/2. Here $ G$ is the infinite-volume Green function of the associated random Schrödinger operator. The main ingredient is a quantitative lower bound on the derivative of the mean effective conductance with respect to the edge weights.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026exponential,
  title = {{Exponential decay of fractional moments in the $H^2|2$ model on $\mathbb Z^2$}},
  author = {Jinglin Wang and Xiaolin Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10982},
  eprint = {2610.10982},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10982},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Exponential decay of fractional moments in the H^2|2 model on ℤ^2
AU  - Jinglin Wang
AU  - Xiaolin Zeng
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.10982
UR  - https://arxiv.org/abs/2610.10982
AB  - For the H^2|2 model on ℤ^2, we show that, at energy zero, the fractional moments of Green functions, 𝔼[ G(x,y)^s] decay exponentially in the distance between x and y, for every constant edge weight W>0 and every 0<s<1/2. Here $ G$ is the infinite-volume Green function of the associated random Schrödinger operator. The main ingredient is a quantitative lower bound on the derivative of the mean effective conductance with respect to the edge weights.
ER  -