For every β>0, the rescaled largest eigenvalues of the minors of a critically spiked Gaussian random matrix converge to a multilevel interlacing particle system built from the Airy-β point process.
Fluctuations of the 2-spin SSK model with magnetic field
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abstract
We analyze the fluctuations of the free energy, replica overlaps, and overlap with the external field in the quadratic spherical SK model with a magnetic field. We identify several different behaviors for these quantities depending on the size of the magnetic field, confirming predictions by Fyodorov-Le Doussal and recent work of Baik, Collins-Wildman, Le Doussal and Wu.
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Multilevel limits of spiked random matrix minors
For every β>0, the rescaled largest eigenvalues of the minors of a critically spiked Gaussian random matrix converge to a multilevel interlacing particle system built from the Airy-β point process.