PreprintCC BY 4.0arXiv
A Linear Variance Bound for Ballistic Deposition
Abstract
We show the height at time t of the standard continuous-time ballistic deposition process has variance at most Cd t, t ≥ 1 in every dimension d ≥ 1. The crucial idea is to adapt a martingale argument due to Aldous, which gives tail bounds on first hitting times for monotone surface growth processes. Inverting these tail bounds and applying a duality theorem due to Penrose yields a linear variance bound for the height of ballistic deposition.
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BibTeX
@misc{sudijono2026linear,
title = {{A Linear Variance Bound for Ballistic Deposition}},
author = {Timothy Sudijono},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24056},
eprint = {2609.24056},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24056},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Linear Variance Bound for Ballistic Deposition
AU - Timothy Sudijono
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24056
UR - https://arxiv.org/abs/2609.24056
AB - We show the height at time t of the standard continuous-time ballistic deposition process has variance at most C_d t, t ≥ 1 in every dimension d ≥ 1. The crucial idea is to adapt a martingale argument due to Aldous, which gives tail bounds on first hitting times for monotone surface growth processes. Inverting these tail bounds and applying a duality theorem due to Penrose yields a linear variance bound for the height of ballistic deposition.
ER -