Localization for Very Sparse Erdös-Rényi Random Graphs (A09)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 470903074

In this project, we analyze the eigenfunctions of the adjacency matrix and the graph Laplacian of Erdös-Rényi random graphs in the very sparse regime where the average number of edges grows proportionally to the number of vertices. The goal is to show that the eigenfunctions are localized by studying the scaling of their inverse participation ratios. In the high-energy regime, we will exploit the known concentration of eigenfunctions at highly connected vertices. We aim to rule out tunneling between them through a combinatorial and percolation-theoretic analysis of their distribution in the giant cluster.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 352: Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
• International Connection: Austria
• Applicant Institution: Ludwig-Maximilians-Universität München
• Project Heads: Professor Laszlo Erdös, Ph.D.; Professor Dr. Markus Heydenreich; Professor Dr. Peter Müller