Zero density of open paths in the Lorentz mirror model for arbitrary mirror probability
Atahualpa S. Kraemer, David P. Sanders
TL;DR
This paper proves that in the Lorentz mirror model, the density of open paths diminishes to zero as the system size grows, regardless of the mirror probability, supported by numerical simulations.
Contribution
It establishes the zero density of open paths in the Lorentz mirror model for all mirror probabilities, combining theoretical proof with numerical evidence.
Findings
Open path density tends to zero as system size increases
Zero density holds for any mirror probability
Numerical simulations support theoretical results
Abstract
We show, incorporating results obtained from numerical simulations, that in the Lorentz mirror model, the density of open paths in any finite box tends to 0 as the box size tends to infinity, for any mirror probability.
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