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Universität Augsburg
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Universität Augsburg
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Professor Dr. Johannes Alt
Bonn
spricht am
Freitag, 30. Oktober 2026
um
16:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| We study the Erdős-Rényi graph, a common random graph model with intricate behaviours. First, I establish a transition in the eigenvector structure of its adjacency matrix. For large enough expected degree, all eigenvectors are delocalized, i.e. their mass spreads out approximately uniformly over all vertices. When the expected degree is small enough, localized eigenvectors emerge. More precisely, the mass of each eigenvector with large eigenvalue is concentrated in a ball around a unique vertex and decays exponentially in the graph distance from this vertex. Second, I determine the Schrödinger time evolution of a free quantum particle hopping on the Erdős-Rényi graph through refined spectral information. Third, I demonstrate that for the corresponding directed Erdős-Rényi graph, all eigenvectors, with eigenvalue away from zero, are delocalized. This is in contrast to the undirected setting in the first part. The talk is based on joint works with Raphael Ducatez, Antti Knowles and Sarah Timhadjelt. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Dominik Schmid |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).