Dmitry A. Timushev

Research Subjects

Research Interests

Dmitry A. Timushev has a total of 12 co-authors. Here are the top co-authors by number of shared publications:

Alexander N. Tikhomirov
Institute of Physics and of Mathematics, Komi Science Center of Ural Branch of RAS, 167982 Syktyvkar, Russia
7 shared publications
Friedrich Götze
Faculty of Mathematics, Bielefeld University, Bielefeld, Germany
4 shared publications
A. A. Naumov
Moscow State University
1 shared publication
A. N. Tikhomirov
Russian Academy of Sciences
1 shared publication
A. V. Nadutkina
Institute of Physics and Mathematics, Komi SC UB RAS, Syktyvkar, Russia
1 shared publication
Alexey Naumov
1 shared publication

Latest Publications

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Cited by 2
- 23 December 2024
- Published by Springer Nature in Journal of Mathematical Sciences
Local Laws for Sparse Sample Covariance Matrices Without the Truncation Condition
by F. Götze, A. N. Tikhomirov, D. A. Timushev
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- 23 December 2024
- Published by Springer Nature in Journal of Mathematical Sciences
Local Laws for Sparse Sample Covariance Matrices Without the Truncation Condition
by F. Götze, A. N. Tikhomirov, D. A. Timushev
Cited by 2
Open Access
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Cited by 1
- 22 July 2024
- Published by MDPI AG in Mathematics
Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks
by Alexander Tikhomirov, Sabina Gulyaeva, Dmitry Timushev
This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices with non-Hermitian blocks.
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- 22 July 2024
- Published by MDPI AG in Mathematics
Open Access
Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks
by Alexander Tikhomirov, Sabina Gulyaeva, Dmitry Timushev
This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution of singular values for the product of independent circulant matrices with non-Hermitian blocks.
Cited by 1
Open Access
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Cited by 1
- 31 May 2024
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
by A. V. Nadutkina, A. N. Tikhomirov, D. A. Timushev
We study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution function of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur distribution function.
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- 31 May 2024
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
Open Access
Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
by A. V. Nadutkina, A. N. Tikhomirov, D. A. Timushev
We study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution function of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur distribution function.
Cited by 1
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- 17 July 2023
- Published by Springer Nature
Rate of Convergence for Sparse Sample Covariance Matrices
by F. Götze, A. Tikhomirov, D. Timushev
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- 17 July 2023
- Published by Springer Nature
Rate of Convergence for Sparse Sample Covariance Matrices
by F. Götze, A. Tikhomirov, D. Timushev
Open Access
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Cited by 3
- 3 July 2022
- Published by MDPI AG in Mathematics
Local Laws for Sparse Sample Covariance Matrices
by Alexander N. Tikhomirov, Dmitry A. Timushev
We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order $n \times m$ with $n / m \to y$ (where $y > 0$ ) and sparse probability $n p_{n} > {log}^{β} n$ (where $β > 0$ ). The bounds of the distance between the empirical spectral distribution function of the sparse sample covariance matrices and the Marchenko–Pastur law distribution function that was obtained in the complex domain $z \in D$ with $Im z > v_{0} > 0$ (where $v_{0}$ ) were of order ${log}^{4} n / n$ and the domain bounds did not depend on $p_{n}$ while $n p_{n} > {log}^{β} n$ .
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- 3 July 2022
- Published by MDPI AG in Mathematics
Open Access
Local Laws for Sparse Sample Covariance Matrices
by Alexander N. Tikhomirov, Dmitry A. Timushev
We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order $n \times m$ with $n / m \to y$ (where $y > 0$ ) and sparse probability $n p_{n} > {log}^{β} n$ (where $β > 0$ ). The bounds of the distance between the empirical spectral distribution function of the sparse sample covariance matrices and the Marchenko–Pastur law distribution function that was obtained in the complex domain $z \in D$ with $Im z > v_{0} > 0$ (where $v_{0}$ ) were of order ${log}^{4} n / n$ and the domain bounds did not depend on $p_{n}$ while $n p_{n} > {log}^{β} n$ .
Cited by 3
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- 1 November 2021
- Published by Pleiades Publishing Ltd in Doklady Mathematics
Local Marchenko–Pastur Law for Sparse Rectangular Random Matrices
by F. Götze, D. A. Timushev, A. N. Tikhomirov
We consider sparse sample covariance matrices with sparsity probability ${{p}_{n}} \geqslant {{c}_{0}}{{\log }^{{\frac{2}{\varkappa }}}}n{\text{/}}n$ with $\varkappa > 0$. Assuming that the distribution of matrix elements has a finite absolute moment of order $4 + \delta $, $\delta > 0$, it is shown that the distance between the Stieltjes transforms of the empirical spectral distribution function and the Marchenko–Pastur law is of order $\log n(1{\text{/}}(nv) + 1{\text{/}}(n{{p}_{n}}))$, where v is the distance to the real axis in the complex plane.
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- 1 November 2021
- Published by Pleiades Publishing Ltd in Doklady Mathematics
Local Marchenko–Pastur Law for Sparse Rectangular Random Matrices
by F. Götze, D. A. Timushev, A. N. Tikhomirov
We consider sparse sample covariance matrices with sparsity probability ${{p}_{n}} \geqslant {{c}_{0}}{{\log }^{{\frac{2}{\varkappa }}}}n{\text{/}}n$ with $\varkappa > 0$. Assuming that the distribution of matrix elements has a finite absolute moment of order $4 + \delta $, $\delta > 0$, it is shown that the distance between the Stieltjes transforms of the empirical spectral distribution function and the Marchenko–Pastur law is of order $\log n(1{\text{/}}(nv) + 1{\text{/}}(n{{p}_{n}}))$, where v is the distance to the real axis in the complex plane.
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Cited by 2
- 1 May 2021
- Published by Pleiades Publishing Ltd in Atmospheric and Oceanic Optics
Granulometric Composition of Settled Aerosol Material and Ratio of Phenolic Compounds in Different-Age Needles
by M. P. Tentukov, V. I. Mikhailov, D. A. Timushev, D. V. Simonenkov, B. D. Belan
We present the results from laser granulometry of a nanosized fraction of aerosol substance and from UV spectrometry of water washouts from different-age needles in four plant species. It is estimated how the hydrothermal conditions influence the time variations in morphometric indices of needles and contamination of their surfaces by phenolic compounds in the composition of secondary organic aerosols. We discuss how secondary organic aerosols are generated on the surfaces of different-age needles during efflorescence of phenolic compounds and their subsequent entry into the forest canopy during turbulent separation of the boundary layer from the leaf surface.
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- 1 May 2021
- Published by Pleiades Publishing Ltd in Atmospheric and Oceanic Optics
Granulometric Composition of Settled Aerosol Material and Ratio of Phenolic Compounds in Different-Age Needles
by M. P. Tentukov, V. I. Mikhailov, D. A. Timushev, D. V. Simonenkov, B. D. Belan
We present the results from laser granulometry of a nanosized fraction of aerosol substance and from UV spectrometry of water washouts from different-age needles in four plant species. It is estimated how the hydrothermal conditions influence the time variations in morphometric indices of needles and contamination of their surfaces by phenolic compounds in the composition of secondary organic aerosols. We discuss how secondary organic aerosols are generated on the surfaces of different-age needles during efflorescence of phenolic compounds and their subsequent entry into the forest canopy during turbulent separation of the boundary layer from the leaf surface.
Cited by 2
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Cited by 40
- 1 August 2018
- Published by Bernoulli Society for Mathematical Statistics and Probability in Bernoulli
On the local semicircular law for Wigner ensembles
by Friedrich Götze, Alexey Naumov, Alexander Tikhomirov, Dmitry Timushev
Project Euclid - mathematics and statistics online
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- 1 August 2018
- Published by Bernoulli Society for Mathematical Statistics and Probability in Bernoulli
On the local semicircular law for Wigner ensembles
by Friedrich Götze, Alexey Naumov, Alexander Tikhomirov, Dmitry Timushev
Project Euclid - mathematics and statistics online
Cited by 40
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Cited by 3
- 1 May 2016
- Published by Pleiades Publishing Ltd in Doklady Mathematics
Local semicircle law under weak moment conditions
by F. Götze, A. A. Naumov, A. N. Tikhomirov, D. A. Timushev
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- 1 May 2016
- Published by Pleiades Publishing Ltd in Doklady Mathematics
Local semicircle law under weak moment conditions
by F. Götze, A. A. Naumov, A. N. Tikhomirov, D. A. Timushev
Cited by 3