### Abstract

In Chap. 1 it is explained that if p is a probability on a finite group G the group matrix X_{G}(p) is a transition matrix for a random walk on G. If f is an arbitrary function on G the process of transforming X_{G}(f) into a block diagonal matrix is equivalent to the obtaining the Fourier transform of f. This chapter explains the connections with harmonic analysis and the group matrix. Most of the discussion is on probability theory and random walks. The fusion of characters discussed in Chap. 4 becomes relevant, and also the idea of fission of characters is introduced, especially those fissions which preserve diaonalizability of the corresponding group matrix. As an example of how the group matrix and group determinant can be used as tools, their application to random walks which become uniform after a finite number of steps is examined.

Original language | English (US) |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 231-270 |

Number of pages | 40 |

DOIs | |

State | Published - Jan 1 2019 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2233 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

*Lecture Notes in Mathematics*(pp. 231-270). (Lecture Notes in Mathematics; Vol. 2233). Springer Verlag. https://doi.org/10.1007/978-3-030-28300-1_7