Question

Applications on limit theorems

Answer 1

Answer:

Anisotropic random walks on the square lattice of the plane could serve as models for the study of transport phenomena of statistical physics. Two-dimensional anisotropic random walks with asymptotic density conditions as in Heyde (J. Statist. Physics 27 (1982), 721-730, and Stochastic Processes. Springer, New York, pp. 125-130) yield fixed column configurations, and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J. Statist. Physics 75 (1994), 891-918) result in random column configurations. We will survey related results in a historical context and, in both cases, also conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane

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