@inproceedings{dcf7635d8ed04cfaaf61b932bba8bd32,
title = "Anomalous random walks and diffusions: From fractals to random media",
abstract = "We present results concerning the behavior of random walks and diffusions on disordered media. Examples treated include fractals and various models of random graphs, such as percolation clusters, trees generated by branching processes, Erdos-R{\'e}nyi random graphs and uniform spanning trees. As a consequence of the inhomogeneity of the underlying spaces, we observe anomalous behavior of the corresponding random walks and diffusions. In this regard, our main interests are in estimating the long time behavior of the heat kernel and in obtaining a scaling limit of the random walk. We will overview the research in these areas chronologically, and describe how the techniques have developed from those introduced for exactly self-similar fractals to the more robust arguments required for random graphs.",
keywords = "Fractals, Heat kernel estimates, Percolation, Random media, Sub-diffusivity",
author = "Takashi Kumagai",
note = "Publisher Copyright: {\textcopyright} 2014 by Seoul ICM 2014 Organizing Committee. All rights reserved.; 2014 International Congress of Mathematicans, ICM 2014 ; Conference date: 13-08-2014 Through 21-08-2014",
year = "2014",
language = "English",
series = "Proceeding of the International Congress of Mathematicans, ICM 2014",
publisher = "KYUNG MOON SA Co. Ltd.",
pages = "75--94",
editor = "Jang, {Sun Young} and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie and Kim, {Young Rock} and Dae-Woong Lee and Ikkwon Yie",
booktitle = "Invited Lectures",
}