207 citations · 2.4k across the 59 of their papers we have counts for
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Fluctuation based proof of the stability of ac spectra of random operators on tree graphs
Michael Aizenman, Robert Sims, Simone Warzel
We summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schrödinger operators…
Persistence under Weak Disorder of AC Spectra of Quasi-Periodic Schroedinger operators on Trees Graphs
Michael Aizenman, Simone Warzel
We consider radial tree extensions of one-dimensional quasi-periodic Schroedinger operators and establish the stability of their absolutely continuous spectra under weak but extens…
Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
Michael Aizenman, Robert Sims, Simone Warzel
We consider the Laplacian on a rooted metric tree graph with branching number and random edge lengths given by independent and identically distributed bounded variable…
Stability of the Absolutely Continuous Spectrum of Random Schroedinger Operators on Tree Graphs
Michael Aizenman, Robert Sims, Simone Warzel
The subject of this work are random Schroedinger operators on regular rooted tree graphs $\T$ with stochastically homogeneous disorder. The operators are of the form $H_λ(ω) = T +…