Anomalous random walks and diffusions: From fractals to random media

Takashi Kumagai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

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-Rényi 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.

Original languageEnglish
Title of host publicationInvited Lectures
EditorsSun Young Jang, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie, Young Rock Kim, Dae-Woong Lee, Ikkwon Yie
PublisherKYUNG MOON SA Co. Ltd.
Pages75-94
Number of pages20
ISBN (Electronic)9788961058070
Publication statusPublished - 2014
Externally publishedYes
Event2014 International Congress of Mathematicans, ICM 2014 - Seoul, Korea, Republic of
Duration: 2014 Aug 132014 Aug 21

Publication series

NameProceeding of the International Congress of Mathematicans, ICM 2014
Volume4

Conference

Conference2014 International Congress of Mathematicans, ICM 2014
Country/TerritoryKorea, Republic of
CitySeoul
Period14/8/1314/8/21

Keywords

  • Fractals
  • Heat kernel estimates
  • Percolation
  • Random media
  • Sub-diffusivity

ASJC Scopus subject areas

  • Mathematics(all)

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