Boundary transmission and excursion geometry in the Lorentz mirror model: a numerical study
Abstract
We study boundary transmission and excursion geometry in the planar Lorentz mirror model through finite-volume numerical experiments. Cylinder penetration quantiles grow approximately linearly with circumference over the simulated range, with a systematic upward drift in the normalized quantiles when vacancies are present. Estimated slab-transmission probabilities yield exponential confinement bounds with quantified statistical confidence at the tested widths. Planar excursions conditioned to reach a distant boundary exhibit transverse ranges proportional to the exit radius, while their repeated-visit fractions vary strongly with mirror density. Endpoint-label collision probabilities substantially exceed a general gluing lower bound, although they account for only part of the observed same-column crossing probability. Finally, rerouting at repeated vertices preserves the exit while substantially shortening the sampled paths. These findings characterize finite-volume transport and excursion geometry without determining an asymptotic scaling exponent or resolving infinite-plane localization.
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BibTeX
@misc{gu2026boundary,
title = {{Boundary transmission and excursion geometry in the Lorentz mirror model: a numerical study}},
author = {Jian Gu and Qin Hao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14949},
eprint = {2609.14949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14949},
}
RIS
TY - UNPB
TI - Boundary transmission and excursion geometry in the Lorentz mirror model: a numerical study
AU - Jian Gu
AU - Qin Hao
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14949
UR - https://arxiv.org/abs/2609.14949
AB - We study boundary transmission and excursion geometry in the planar Lorentz mirror model through finite-volume numerical experiments. Cylinder penetration quantiles grow approximately linearly with circumference over the simulated range, with a systematic upward drift in the normalized quantiles when vacancies are present. Estimated slab-transmission probabilities yield exponential confinement bounds with quantified statistical confidence at the tested widths. Planar excursions conditioned to reach a distant boundary exhibit transverse ranges proportional to the exit radius, while their repeated-visit fractions vary strongly with mirror density. Endpoint-label collision probabilities substantially exceed a general gluing lower bound, although they account for only part of the observed same-column crossing probability. Finally, rerouting at repeated vertices preserves the exit while substantially shortening the sampled paths. These findings characterize finite-volume transport and excursion geometry without determining an asymptotic scaling exponent or resolving infinite-plane localization.
ER -