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.

arXiv comment30 pages, 9 figures, 1 table

References in corpus (1)

• Explicit Construction of the Brownian Self-Transport Operator

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