91 citations · 323 across the 30 of their papers we have counts for
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Recent results of quantum ergodicity on graphs and further investigation
Nalini Anantharaman, Mostafa Sabri
We outline some recent proofs of quantum ergodicity on large graphs and give new applications in the context of irregular graphs. We also discuss some remaining questions.
Quantum Ergodicity on Graphs : from Spectral to Spatial Delocalization
Nalini Anantharaman, Mostafa Sabri
We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of Schrödinger operators in a very general setting. We consider a sequence of finite graphs endowed with d…
Quantum ergodicity for the Anderson model on regular graphs
Nalini Anantharaman, Mostafa Sabri
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. pur…
Some relations between the spectra of simple and non-backtracking random walks
Nalini Anantharaman
We establish some relations between the spectra of simple and non-backtracking random walks on non-regular graphs, generalizing some well-known facts for regular graphs. Our two ma…