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Palm Disintegration and Height-Profile Recovery for Projected Hardy--Szegő Zeros

  • Feng Guo
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Abstract

We study the horizontal projection of the upper-half-plane Hardy--Szegő zero process after independent height-dependent thinning, with height retained as an unobserved mark. We identify the reduced Palm law of the projected process by disintegrating over the missing height coordinate, describe the conditional law of the two heights associated with a pair of projected points and its near- and far-separation limits, and obtain the small-spacing asymptotic for the right nearest neighbour. We then study recovery of the height profile from the projected second-order structure. The resulting covariance transform uniquely determines every compactly supported finite positive height measure and, for separated finite unions of intervals, yields uniform Lipschitz recovery of all endpoints, even when the number of intervals is unknown but bounded.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026palm,
  title = {{Palm Disintegration and Height-Profile Recovery for Projected Hardy--Szegő Zeros}},
  author = {Feng Guo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15174},
  eprint = {2609.15174},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15174},
}
RIS
TY  - UNPB
TI  - Palm Disintegration and Height-Profile Recovery for Projected Hardy--Szegő Zeros
AU  - Feng Guo
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15174
UR  - https://arxiv.org/abs/2609.15174
AB  - We study the horizontal projection of the upper-half-plane Hardy--Szegő zero process after independent height-dependent thinning, with height retained as an unobserved mark. We identify the reduced Palm law of the projected process by disintegrating over the missing height coordinate, describe the conditional law of the two heights associated with a pair of projected points and its near- and far-separation limits, and obtain the small-spacing asymptotic for the right nearest neighbour. We then study recovery of the height profile from the projected second-order structure. The resulting covariance transform uniquely determines every compactly supported finite positive height measure and, for separated finite unions of intervals, yields uniform Lipschitz recovery of all endpoints, even when the number of intervals is unknown but bounded.
ER  -