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Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement
Stephane Dartois, Benjamin McKenna
The injective norm is a natural generalization to tensors of the operator norm of a matrix. In quantum information, the injective norm is one important measure of genuine multipart…
Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime
Sofiia Dubova, Yue M. Lu, Benjamin McKenna +1
We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function applied entrywise to a sample-covari…
Large deviations for the largest eigenvalue of generalized sample covariance matrices
Jonathan Husson, Benjamin McKenna
We establish a large-deviations principle for the largest eigenvalue of a generalized sample covariance matrix, meaning a matrix proportional to , where has i.i.d. real…
Extremal statistics of quadratic forms of GOE/GUE eigenvectors
Laszlo Erdos, Benjamin McKenna
We consider quadratic forms of deterministic matrices evaluated at the random eigenvectors of a large GOE or GUE matrix, or equivalently evaluated at the columns o…