Explicit Construction of the Brownian Self-Transport Operator

Details Explicit Construction of the Brownian Self-Transport Operator Explicit Construction of the Brownian Self-Transport Operator

2002-04-17

arxiv.org/abs/math/0204215v1

Mathematics

Probability

30 pages, 9 figures, 1 table

Scientific paper

10.1140/epjb/e2003-00339-4

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.

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