Quantum ergodicity on regular graphs

DOI10.1007/s00220-017-2879-9zbMath1368.58015arXiv1512.06624OpenAlexW2611458856MaRDI QIDQ2358809

Nalini Anantharaman

Publication date: 16 June 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06624

zbMATH Keywords

regular graphsquantum ergodicityanisotropic random walks

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Sums of independent random variables; random walks (60G50) Quantum chaos (81Q50) Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity (58J51)

Related Items (17)

The necessity of conditions for graph quantum ergodicity and Cartesian products with an infinite graph ⋮ Benjamini-Schramm convergence and spectra of random hyperbolic surfaces of high genus ⋮ Cayley graphs that have a quantum ergodic eigenbasis ⋮ Quantum ergodicity for periodic graphs ⋮ Local Kesten-McKay law for random regular graphs ⋮ Quantum ergodicity for large equilateral quantum graphs ⋮ Pointwise Weyl law for graphs from quantized interval maps ⋮ Spectrum of random d‐regular graphs up to the edge ⋮ Probability and entanglement evolutions for Szegedy's quantum search on the one-dimensional cycle with self-loops ⋮ Quantum ergodicity for the Anderson model on regular graphs ⋮ Poisson kernel expansions for Schrödinger operators on trees ⋮ Eigenstate thermalization hypothesis for Wigner matrices ⋮ Quantum ergodicity for expanding quantum graphs in the regime of spectral delocalization ⋮ Recent results of quantum ergodicity on graphs and further investigation ⋮ \(L^p\) norms and support of eigenfunctions on graphs ⋮ Quantum ergodicity on graphs: from spectral to spatial delocalization ⋮ Eigenvalues of random lifts and polynomials of random permutation matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Quantum ergodicity for quantum graphs without back-scattering
• Cutoff on all Ramanujan graphs
• Eigenfunction statistics on quantum graphs
• Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs
• Ergodicity and eigenfunctions of the Laplacian
• Uniform distribution of eigenfunctions on compact hyperbolic surfaces
• Ramanujan graphs
• The expected eigenvalue distribution of a large regular graph
• Every connected regular graph of even degree is a Schreier coset graph
• Value distribution of the eigenfunctions and spectral determinants of quantum star graphs
• No quantum ergodicity for star graphs
• Recurrence of distributional limits of finite planar graphs
• Semi-classical measures on quantum graphs and the Gauß map of the determinant manifold
• Quantum ergodicity on large regular graphs
• Quantum ergodicity for graphs related to interval maps
• Symmetric Random Walks on Groups
• Eigenvectors of the discrete Laplacian on regular graphs—a statistical approach
• The range of the Helgason-Fourier transformation on homogeneous trees
• Harmonic analysis for anisotropic random walks on homogeneous trees
• Quantum Ergodicity and Averaging Operators on the Sphere
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE

This page was built for publication: Quantum ergodicity on regular graphs