Latest Advances in Random Walks Dating Back to One Hundred Years
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".
Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 8490
Special Issue Editor
Interests: random walks; Markov chains; causality; diffusion; fractals; networks; mathematical models in computational neuroscience
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Special Issue Information
Dear Colleagues,
Random walks on graphs may be the simplest stochastic process. Thanks to their simplicity, they serve as a model in many areas beyond probability. Among others, they are the fundamental model of diffusion in physics. The first astonishing observation was made by György Pólya in 1921 about the recurrence of the random walk on d-dimensional lattice. Numerous great mathematicians have since then contributed to the development of its theory, such as Paul Erdős, Alfréd Rényi, A. Doverczky, A. Kakutani, W. Feller,Y.G. Sinai, R.L. Dobrushin, D. Aldous, S. Redner. G. Weiss, F. Den Hollander, H. Kesten, F. Solomon, W. Woess, B.D. Hughes, P.G. Doyle, J.L. Snell, S. Alexander, R.Orbach, R. Rammal, G. Toulouse, G.F. Lawler, N. Madras, G. Slade, L. Lovász, P. Révész, J. Norris, V.A. Kaimanovitch, A. Grigor’yan, L. Saloff-Coste, T. Coulhon, O. Zeitouni, G. Kozma, and Y. Peres, just to name some. Recent advances have widened the picture to sub- and superdiffusive phenomena, metastability, and stock price movements, again to name only a fraction of the options.
The aim of the present Special Issue is to provide a wide spectrum but at the same time deep insight into recent results with respect to random walk on its own, as well as its essential applications. We seek papers which provide new and striking insight into the nature of random walk or phenomena modelled by random walk. The emphasis is on the interesting phenomenon in the spirit of György Pólya, not on incremental technical advances. Survey papers might be accommodated in the Special Issue, one for each specific broad area such as RWs on graphs, RWs in random environments, RWs in physics, chemistry, biology, economics, etc.
András Telcs
Guest Editor
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Keywords
- Random walks
- Random walks on graphs
- Random walks on fractals
- Random walks in science