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of 2 612
pro vyhledávání: '"60B20"'
We study the sensitivity of the eigenvectors of random matrices, showing that even small perturbations make the eigenvectors almost orthogonal. More precisely, we consider two deformed Wigner matrices $W+D_1$, $W+D_2$ and show that their bulk eigenve
Externí odkaz:
http://arxiv.org/abs/2410.10718
We consider two Hamiltonians that are close to each other, $H_1 \approx H_2 $, and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle \psi_0, \mathrm{e}^{\mathrm{i} t H_2} \mathrm{e}^{-\mathrm{i} t H_1} \psi_0 \ra
Externí odkaz:
http://arxiv.org/abs/2410.08108
For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singulari
Externí odkaz:
http://arxiv.org/abs/2410.06813
Autor:
Mai, Xiaoyi, Liao, Zhenyu
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To relax this res
Externí odkaz:
http://arxiv.org/abs/2410.05609
Autor:
Lancien, Cécilia
In this work we investigate how quantum expanders (i.e. quantum channels with few Kraus operators but a large spectral gap) can be constructed from unitary designs. Concretely, we prove that a random quantum channel whose Kraus operators are independ
Externí odkaz:
http://arxiv.org/abs/2409.17971
Autor:
Brooks, Thomas G.
Efficient schemes for sampling from the eigenvalues of the Wishart distribution have recently been described for both the uncorrelated central case (where the covariance matrix is $\mathbf{I}$) and the spiked Wishart with a single spike (where the co
Externí odkaz:
http://arxiv.org/abs/2410.05280
Autor:
Vengerovsky, Valentin
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices in each c
Externí odkaz:
http://arxiv.org/abs/2409.18148
For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof of the thi
Externí odkaz:
http://arxiv.org/abs/2409.17030
Autor:
Alt, Johannes, Krüger, Torben
We consider the Brown measure of $a+\mathfrak{c}$, where $a$ lies in a commutative tracial von Neumann algebra $\mathcal{B}$ and $\mathfrak{c}$ is a $\mathcal{B}$-valued circular element. Under certain regularity conditions on $a$ and the covariance
Externí odkaz:
http://arxiv.org/abs/2409.15405
The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these propertie
Externí odkaz:
http://arxiv.org/abs/2409.14560