Non-ergodic delocalization in the Rosenzweig-Porter model

DOI10.1007/s11005-018-1131-7zbMath1408.60012arXiv1709.10313OpenAlexW2760640517WikidataQ129071646 ScholiaQ129071646MaRDI QIDQ1737092

Simone Warzel, Per von Soosten

Publication date: 26 March 2019

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

Full work available at URL: https://arxiv.org/abs/1709.10313

zbMATH Keywords

characteristicsnon-ergodicityresolvent flowRosenzweig-Porter model

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) PDEs in connection with quantum mechanics (35Q40) Random matrices (algebraic aspects) (15B52)

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Cites Work

• Averaging fluctuations in resolvents of random band matrices
• The eigenvector moment flow and local quantum unique ergodicity
• Local semicircle law and complete delocalization for Wigner random matrices
• The analogues of entropy and of Fisher's information measure in free probability theory. I
• Processes with free increments
• The phase transition in the ultrametric ensemble and local stability of Dyson Brownian motion
• Fixed energy universality of Dyson Brownian motion
• Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices
• Convergence of local statistics of Dyson Brownian motion
• Eigenvector statistics of sparse random matrices
• A STOCHASTIC GRONWALL LEMMA
• Existence and uniqueness of solutions of stochastic functional differential equations
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• On Mesoscopic Equilibrium for Linear Statistics in Dyson’s Brownian Motion
• A Dynamical Approach to Random Matrix Theory
• Local deformed semicircle law and complete delocalization for Wigner matrices with random potential