Hypergroups and distance distributions of random walks on graphs

  • Kenta Endo
  • Ippei Mimura
  • Yusuke Sawada

Abstract

Wildberger's construction enables us to obtain a hypergroup from a random walk on a special graph. We will give a probability theoretic interpretation to products on the hypergroup. The hypergroup can be identified with a commutative algebra whose basis is transition matrices. We will estimate the operator norm of such a transition matrix and clarify a relationship between their matrix products and random walks.

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Published
2021-02-17
How to Cite
Endo, K., Mimura, I., & Sawada, Y. (2021). Hypergroups and distance distributions of random walks on graphs. MATHEMATICA SCANDINAVICA, 127(1), 43-62. https://doi.org/10.7146/math.scand.a-122932
Section
Articles