A limit theorem at the spectral edge for corners of time-dependent Wigner matrices

Abstract

For the eigenvalues of principal submatrices of stochastically evolving Wigner matrices, we construct and study the edge scaling limit: a random decreasing sequence of continuous functions of two variables, which at every point has the distribution of the Airy point process. The analysis is based on the methods developed by Soshnikov to study the extreme eigenvalues of a single Wigner matrix.

37 pages; v2: revised the presentation and fixed lapses; v3: added minor clarifications

References in corpus (6)

• Invariant $\beta$-ensembles and the Gauss-Wigner crossover
• A Necessary and Sufficient Condition for Edge Universality of Wigner matrices
• From Alternating Sign Matrices to the Gaussian Unitary Ensemble
• A diffusive matrix model for invariant $\beta$-ensembles
• On the partial connection between random matrices and interacting particle systems
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Cited by in corpus (3)

• A Limit Theorem for Stochastically Decaying Partitions at the Edge
• A convergence framework for Airy${}_{\beta }$ line ensemble via pole evolution
• The geometry of coalescing random walks, the Brownian web distance and KPZ universality