Abstract
In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ℤd (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d⩾2.
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References
J. L. Lebowitz, Talk at the Conference on Random Fields, in Esztergom, Hungary, 1979.
H. van Beijeren and H. Spohn (to be published).
F. Spitzer,Principles of Random Walk (Princeton University Press, Princeton, New Jersey, 1964).
P. Billingsley,Convergence of Probability Measures, (Wiley, New York, 1968).
Ya. G. Sinai, Limit Theorem for a Random Walk in a One-Dimensional Random Environment (to be published).
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Szász, D., Telcs, A. Random walk in an inhomogeneous medium with local impurities. J Stat Phys 26, 527–537 (1981). https://doi.org/10.1007/BF01011433
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DOI: https://doi.org/10.1007/BF01011433