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