Abstract
We study the random motion of a tracer particle in a two-dimensional dense lattice gas. Repeated encounters of asingle vacancy displace the tracer particle from its initial position by a vector y of which we calculate the time-dependent distributionP t(y). On an infinite lattice and for large times
whereK 0 is a modified Bessel function. The same problem is studied on a finiteL×L lattice with periodic boundary conditions; thereP t(y) is shown to be a Gaussian on a time scaleL 2 InL. On an ∞×L strip and for large times,P t(y) is an explicitly given (but nonelementary) function of the scaling variable ξy 1/t 1/4, identical to the function occurring in the problem of a random walker on a random one-dimensional path.
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Brummelhuis, M.J.A.M., Hilhorst, H.J. Single-vacancy induced motion of a tracer particle in a two-dimensional lattice gas. J Stat Phys 53, 249–278 (1988). https://doi.org/10.1007/BF01011556
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DOI: https://doi.org/10.1007/BF01011556