Explicit Construction of the Brownian Self-Transport Operator

Abstract

Applying the technique of characteristic functions developped for one-dimensional regular surfaces (curves) with compact support, we obtain the distribution of hitting probabilities for a wide class of finite membranes on square lattice. Then we generalize it to multi-dimensional finite membranes on hypercubic lattice. Basing on these distributions, we explicitly construct the Brownian self-transport operator which governs the Laplacian transfer. In order to verify the accuracy of the distribution of hitting probabilities, numerical analysis is carried out for some particular membranes.

30 pages, 9 figures, 1 table

References in corpus (1)

• Explicit Construction of the Brownian Self-Transport Operator

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