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math-ph2026
Quantum percolation conjecture on regular trees
Simon Becker, Izak Oltman
For Bernoulli bond percolation on every regular tree of degree at least three, we prove that infinite clusters appear strictly before absolutely continuous spectrum. Throughout an…
math-ph2026
Disorder on the hyperbolic square lattice I: Anderson delocalization and absolutely continuous spectrum
Simon Becker, Izak Oltman
We study the Anderson model on hyperbolic lattices. The graph is the Cartesian product of the Euclidean lattice with the regular hyperbolic square lattice having five squares at ea…
math.SP2026
Spectra of Non-Self-Adjoint Almost Mathieu Matrices and the Scottish Flag Operator
Simon Becker, Izak Oltman
For and a potential phase , we study the non-self-adjoint almost Mathieu matrix obtained by multiplying the discrete Laplacian by a complex phase…