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Category: <span>Specftral theory</span>
Home Archive for category "Specftral theory"

Category: Specftral theory

More Quiver Math
Graph theory, Specftral theory

More Quiver Math

By oliverknill August 7, 2022 August 7, 2022

The paper [PDF] on the upper bound is updated a bit. It will also be updated on the ArXiv. In the video below, there is an update. Both for quivers as well as non-magnetic quivers (quivers without multiple connections), we can use induction to prove results. One of the amendments …

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Schroedinger operators on Graphs
Graph theory, Specftral theory

Schroedinger operators on Graphs

By oliverknill July 25, 2022 July 26, 2022

Quivers allow to model Schroedinger operators on graphs. With loops we can modify scalar values on vertices, with multiple connections, we can modify the magnetic part. This makes quivers attractive as well as theorems about quivers more interesting. An example was . In the talk last Saturday, I also mentioned …

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The Upper bound Spectral Theorem
Graph theory, Specftral theory

The Upper bound Spectral Theorem

By oliverknill July 10, 2022 July 12, 2022

In my theorem telling that the k-th largest eigenvalue for the Kirchhoff Laplacian of a finite simple graph satisfies the bound I use a lemma which generalizes the Andrson-Morley super symmetry result of 1985. That paper had provided a ground breaking upper bound for the spectral radius . The proof …

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