Tight anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) is established for non-Hermitian M-QSP, with impossibility of √(β_I T) fast-forwarding, new angle-finding algorithms, and extensions to time-dependent cases.
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Moderate-frequency Floquet driving in a quasiperiodic Ising chain suppresses many-body localization and proliferates the many-body critical phase.
For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.
An iterative algorithm combining adaptive Marčenko–Pastur edge recalibration with a participation-ratio delocalization filter recovers weak global factors near the BBP transition in high-dimensional financial correlation matrices.
Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.
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Optimal Bounds, Barriers, and Extensions for Non-Hermitian Bivariate Quantum Signal Processing
Tight anti-Hermitian query complexity d_I = Θ(β_I T + log(1/ε)/log log(1/ε)) is established for non-Hermitian M-QSP, with impossibility of √(β_I T) fast-forwarding, new angle-finding algorithms, and extensions to time-dependent cases.
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Floquet-induced suppression of thermalization in a quasiperiodic Ising chain
Moderate-frequency Floquet driving in a quasiperiodic Ising chain suppresses many-body localization and proliferates the many-body critical phase.
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The Tracy-Widom distribution at large Dyson index
For large beta the TW density takes the form exp(-beta Phi(a)) with Phi(a) obtained as the solution of a Painleve II equation via saddle-point analysis of the stochastic Airy operator.
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Iterative detection of global factors near the BBP phase transition
An iterative algorithm combining adaptive Marčenko–Pastur edge recalibration with a participation-ratio delocalization filter recovers weak global factors near the BBP transition in high-dimensional financial correlation matrices.
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Lecture notes on random matrix theory: the results, the applications, and the analytical tools
Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.