Year: 2025
Type: preprint
Abstract: In this article we prove a sprinkled decoupling inequality for the stationary Hammersley's interacting particle process. Inspired by the work of Baldasso and Texeira (2018), and Hilário, Kious and Texeira (2020), we apply this inequality to study two distinct problems on the top of this particle process. First, we analyze a detection problem, demonstrating that a fugitive can evade particles, provided that their jump range is sufficiently large. Second, we show that a random walk in a dynamic random environment exhibits ballistic behavior with respect to the characteristic speed of the particle system, under a weak assumption on the probability of being away of this critical speed.
Source: arXiv (Cornell University)
Authors: Pimentel, Leandro P. R., Viveros, Roberto
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414682157
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