52 citations · 180 across the 41 of their papers we have counts for
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A note on the tensor product of two random unitary matrices
Tomasz Tkocz
In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the proc…
S-inequality for certain product measures
Piotr Nayar, Tomasz Tkocz
In this paper we prove the S-inequality for certain product probability measures and ideals in R^n . As a result, for the Weibull and Gamma product distributions we derive concentr…
Extremal spacings between eigenphases of random unitary matrices and their tensor products
Marek Smaczynski, Tomasz Tkocz, Marek Kus +1
Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spa…
Tensor Products of Random Unitary Matrices
Tomasz Tkocz, Marek Smaczynski, Marek Kus +2
Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random mat…
The unconditional case of the complex S-inequality
Piotr Nayar, Tomasz Tkocz
In this note we prove the complex counterpart of the S-inequality for complete Reinhardt sets. In particular, this result implies that the complex S-inequality holds for unconditio…
A Note on a Brunn-Minkowski Inequality for the Gaussian Measure
Piotr Nayar, Tomasz Tkocz
We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.