Exact mean first-passage time on the T-graph
TL;DR: The explicit expression for taug is found as a function of the generation g and of the volume V of the underlying fractal of the T-fractal by means of analytic techniques based on decimation procedures.
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Abstract: We consider a simple random walk on the T-fractal and we calculate the exact mean time taug to first reach the central node i0. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except i0. By means of analytic techniques based on decimation procedures, we find the explicit expression for taug as a function of the generation g and of the volume V of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.
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References
A Guide to First-Passage Processes by Sidney Redner
Sidney Redner
- 01 Aug 2001
Abstract: Preface Errata 1. First-passage fundamentals 2. First passage in an interval 3. Semi-infinite system 4. Illustrations of first passage in simple geometries 5. Fractal and nonfractal networks 6. Systems with spherical symmetry 7. Wedge domains 8. Applications to simple reactions References Index.
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•Book
A guide to first-passage processes
Sidney Redner
- 01 Jan 2001
TL;DR: In this article, first passage in an interval is illustrated in simple geometries, and the first passage is in a semi-infinite system and a non-fractal system.
•Book
Diffusion and Reactions in Fractals and Disordered Systems
Daniel ben-Avraham,Shlomo Havlin +1 more
- 20 Nov 2000
TL;DR: In this paper, the authors present an exact solvable model of coalescence and the IPDF method to represent the dynamics of random walks and diffusion in the Sierpinski gasket.
First-passage times in complex scale-invariant media
TL;DR: The analytical approach provides a universal scaling dependence of the mean FPT on both the volume of the confining domain and the source–target distance, which is applicable to a broad range of stochastic processes characterized by length-scale-invariant properties.