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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/18900
Generalization of the persistent random walk to dimensions greater than 1
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We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.
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BOGUÑÁ, Marián, PORRÀ I ROVIRA, Josep Maria and MASOLIVER, Jaume. Generalization of the persistent random walk to dimensions greater than 1. Physical Review E. 1998. Vol. 58, num. 6, pags. 6992-6998. ISSN 1539-3755. [consulted: 8 of October of 2026]. Available at: https://hdl.handle.net/2445/18900