Recent results of quantum ergodicity on graphs and further investigation
From MaRDI portal
Publication:2292302
DOI10.5802/afst.1609zbMath1434.82037arXiv1711.07666OpenAlexW2768863795MaRDI QIDQ2292302
Mostafa Sabri, Nalini Anantharaman
Publication date: 3 February 2020
Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1711.07666
Random graphs (graph-theoretic aspects) (05C80) Random matrices (probabilistic aspects) (60B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random linear operators (47B80) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)
Related Items
Dispersion for Schrödinger operators on regular trees ⋮ The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph ⋮ Absolutely continuous spectrum for quantum trees ⋮ Existence of absolutely continuous spectrum for Galton-Watson random trees ⋮ Quantum ergodicity for periodic graphs ⋮ Flat bands of periodic graphs ⋮ Quantum ergodicity for large equilateral quantum graphs ⋮ \(L^p\) norms and support of eigenfunctions on graphs ⋮ Around quantum ergodicity
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Cutoff on all Ramanujan graphs
- Absolutely continuous spectrum for random operators on trees of finite cone type
- Spectral statistics of Erdős-Rényi graphs. I: Local semicircle law
- Cover time of a random graph with given degree sequence
- Expansion of random graphs: new proofs, new results
- On the limit of large girth graph sequences
- Quantum ergodicity and Benjamini-Schramm convergence of hyperbolic surfaces
- Ergodicity and eigenfunctions of the Laplacian
- Uniform distribution of eigenfunctions on compact hyperbolic surfaces
- Ramanujan graphs
- Extended states in the Anderson model on the Bethe lattice
- Relative expanders or weakly relatively Ramanujan graphs.
- Not every uniform tree covers Ramanujan graphs
- Mean quantum percolation
- Poisson kernel expansions for Schrödinger operators on trees
- Nonbacktracking spectrum of random graphs: community detection and nonregular Ramanujan graphs
- Absolutely continuous spectrum for multi-type Galton-Watson trees
- Point spectrum on a quasi homogeneous tree
- Recurrence of distributional limits of finite planar graphs
- On the spectral theory of trees with finite cone type
- Quantum ergodicity on graphs: from spectral to spatial delocalization
- Quantum ergodicity on large regular graphs
- Quantum ergodicity on regular graphs
- Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
- Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
- Local Kesten-McKay law for random regular graphs
- Processes on unimodular random networks
- Probability on Trees and Networks
- Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs
- A new proof of Friedman's second eigenvalue theorem and its extension to random lifts
- Basic Complex Analysis
- NON-BACKTRACKING RANDOM WALKS MIX FASTER
- A proof of Alon’s second eigenvalue conjecture and related problems
- Reversibility of a simple random walk on periodic trees
- Non-Backtracking Random Walks and Cogrowth of Graphs
- Quantum Ergodicity and Averaging Operators on the Sphere
- Recovery and Rigidity in a Regular Stochastic Block Model
- The Asymptotic Number of Unlabelled Regular Graphs
- Unimodular random trees
- Quantum ergodicity for the Anderson model on regular graphs
