• Corpus ID: 222178214

Quantum graphs -- Generic eigenfunctions and their nodal count and Neumann count statistics

  title={Quantum graphs -- Generic eigenfunctions and their nodal count and Neumann count statistics},
  author={Lior Alon},
  journal={arXiv: Mathematical Physics},
  • Lior Alon
  • Published 6 October 2020
  • Mathematics
  • arXiv: Mathematical Physics
In this thesis, we study Laplacian eigenfunctions on metric graphs, also known as quantum graphs. We restrict the discussion to standard quantum graphs. These are finite connected metric graphs with functions that satisfy Neumann vertex conditions. The first goal of this thesis is the study of the nodal count problem. That is the number of points on which the $n$th eigenfunction vanishes. We provide a probabilistic setting using which we are able to define the nodal count\textquoteright s… 
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