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pro vyhledávání: '"Pastur, Leonid"'
We study the stochastic dynamics of a two-dimensional particle assuming that the components of its position are two coupled random-acceleration processes evolving in a confining parabolic potential and are the subjects of independent Gaussian white n
Externí odkaz:
http://arxiv.org/abs/2309.10807
Autor:
Pastur, Leonid1,2 (AUTHOR) pastur2001@yahoo.com, Slavin, Victor2 (AUTHOR)
Publikováno v:
Entropy. Jul2024, Vol. 26 Issue 7, p564. 23p.
Autor:
Pastur, Leonid
The paper deals with the distribution of singular values of the input-output Jacobian of deep untrained neural networks in the limit of their infinite width. The Jacobian is the product of random matrices where the independent rectangular weight matr
Externí odkaz:
http://arxiv.org/abs/2201.04543
Autor:
Bratus, Ekaterina, Pastur, Leonid
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of lar
Externí odkaz:
http://arxiv.org/abs/2005.05222
Autor:
Pastur, Leonid
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important difference is that
Externí odkaz:
http://arxiv.org/abs/2001.06188
Publikováno v:
Commun. Math. Phys. 376, 649-679 (2020); Erratum: ibid. 382, 655-656 (2021)
We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a criti
Externí odkaz:
http://arxiv.org/abs/1903.05057
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Consider a random non-centered multiple antenna radio transmission channel. Assume that the deterministic part of the channel is itself frequency selective, and that the random multipath part is represented by an ergodic stationary vector process. In
Externí odkaz:
http://arxiv.org/abs/1504.00847
Autor:
Lytova, Anna, Pastur, Leonid
An equation is obtained for the Stieltjes transform of the normalized distribution of singular values of non-symmetric band random matrices in the limit when the band width and rank of the matrix simultaneously tend to infinity. Conditions under whic
Externí odkaz:
http://arxiv.org/abs/1503.04353
Autor:
Lebowitz, Joel L., Pastur, Leonid
We consider a random matrix model of interaction between a small $n$-level system, $S$, and its environment, a $N$-level heat reservoir, $R$. The interaction between $S$ and $R$ is modeled by a tensor product of a fixed $% n\times n$ matrix and a $N\
Externí odkaz:
http://arxiv.org/abs/1502.05004