Fractional Dynamics on Networks and Lattices

Fractional Dynamics on Networks and Lattices

EnglishEbook
Michelitsch, Thomas
WILEY
EAN: 9781119608219
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CZK 4,278
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Detailed information

This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local fractional walks with the emergence of L vy flights. In Part 2, fractional dynamics and L vy flight behavior are analyzed thoroughly, and a generalization of P lya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.
EAN 9781119608219
ISBN 111960821X
Binding Ebook
Publisher WILEY
Publication date April 10, 2019
Language English
Country Uruguay
Authors Collet, Bernard; Michelitsch, Thomas; Nicolleau, Franck; Nowakowski, Andrzej; Riascos, Alejandro Perez
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