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PreprintCC BY 4.0arXiv

Aperiodic random walks: uniform estimates, local limits and invariance principles

  • Jiaming Xu
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Abstract

We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uniform exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zero endpoints. The increment law may vary with the scaling parameter.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026aperiodic,
  title = {{Aperiodic random walks: uniform estimates, local limits and invariance principles}},
  author = {Jiaming Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.02257},
  eprint = {2609.02257},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02257},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Aperiodic random walks: uniform estimates, local limits and invariance principles
AU  - Jiaming Xu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.02257
UR  - https://arxiv.org/abs/2609.02257
AB  - We prove uniform endpoint estimates, killed local limits, and conditioned-bridge invariance principles for triangular arrays of centered, aperiodic, integer-valued random walks with uniform exponential tails. The endpoint estimates cover all nonnegative heights, while the local limits treat positive diffusive and zero endpoints. The increment law may vary with the scaling parameter.
ER  -