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Singularly continuous spectrum of a self-similar Laplacian on the half-line

Journal of Mathematical Physics, ISSN: 0022-2488, Vol: 57, Issue: 5
2016
  • 13
    Citations
  • 0
    Usage
  • 5
    Captures
  • 0
    Mentions
  • 0
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Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    13
    • Citation Indexes
      13
  • Captures
    5

Article Description

We investigate the spectrum of the self-similar Laplacian, which generates the so-called "pq random walk" on the integer half-line Z. Using the method of spectral decimation, we prove that the spectral type of the Laplacian is singularly continuous whenever p ≠ 1/2. This serves as a toy model for generating singularly continuous spectrum, which can be generalized to more complicated settings. We hope it will provide more insight into Fibonacci-type and other weakly self-similar models.

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