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The Manhattan and Lorentz Mirror Models -- A result on the Cylinder with low density of mirrors

Published 7 Oct 2020 in math.PR, math-ph, and math.MP | (2010.03609v1)

Abstract: We study the Manhattan and Lorentz Mirror models on an infinite cylinder of finite even width $n$, with the mirror probability $p$ satisfying $p<Cn{-1}$, $C$ a constant. We use the Brauer and Walled Brauer algebras to show that the maximum height along the cylinder reached by a walker is order $p{-2}$.

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