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Media type:
E-Book;
Thesis
Title:
Random environments and the percolation model
:
non-dissipative fluctuations of random walk process on finite size clusters
Other titles:
Übersetzung des Haupttitels: Zufallsumgebungen und das Perkolationsmodell: nicht-dissipative Fluktuationen des Random-Walk-Prozesses bei endlichen Clustern
University thesis:
Dissertation, Universität Potsdam, 2020
Footnote:
kumulative Dissertation
Description:
Percolation process, which is intrinsically a phase transition process near the critical point, is ubiquitous in nature. Many of its applications embrace a wide spectrum of natural phenomena ranging from the forest fires, spread of contagious diseases, social behaviour dynamics to mathematical finance, formation of bedrocks and biological systems. The topology generated by the percolation process near the critical point is a random (stochastic) fractal. It is fundamental to the percolation theory that near the critical point, a unique infinite fractal structure, namely the infinite cluster, would emerge. As de Gennes suggested, the properties of the infinite cluster could be deduced by studying the dynamical behaviour of the random walk process taking place on it. He coined the term the ant in the labyrinth. The random walk process on such an infinite fractal cluster exhibits a subdiffusive dynamics in the sense that the mean squared displacement grows as ~t2/dw, where dw, called the fractal dimension of the random walk path, is ...