Random Walks on Topological Crystals

  • Toshikazu Sunada
Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 6)


The most exciting moment we encounter while studying mathematics is when we observe that a seemingly isolated subject turns out to be connected with other fields in an unexpected way. In the present and next chapters, we shall give two such examples in connection with standard realizations. The first is asymptotic analysis of random walks on topological crystals which motivated the author to introduce the concept of standard realization [58, 60], and is the theme of this chapter. The second, to be explained in the next chapter, is a discrete (combinatorial) analogue of classical algebraic geometry, a field of more recent vintage, in which the standard realizations in a processed form show up as an analogue of the Abel–Jacobi map.


Random Walk Quantum Walk Simple Random Walk Base Graph Unitary Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Japan 2013

Authors and Affiliations

  • Toshikazu Sunada
    • 1
  1. 1.School of Science and TechnologyMeiji UniversityKawasaki-shiJapan

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