Alexander N. Tikhomirov
Research Subjects
Alexander N. Tikhomirov has a total of 22 co-authors. Here are the top co-authors by number of shared publications:
- Friedrich Götze
Faculty of Mathematics, Bielefeld University, Bielefeld, Germany
14 shared publications - Dmitry A. Timushev
Komi Science Center of Ural Division of RAS, Syktyvkar, Russia
7 shared publications F. Götze
Faculty of Mathematics, University of Bielefeld, Bielefeld, Germany
7 shared publicationsFriedrich Götze
5 shared publications- Friedrich Götze
Universität Bielefeld
4 shared publications - Nikita Alexeev
ITMO University
4 shared publications
Latest Publications
- 22 December 2025
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
- Vol. 35 (4) , 343-355
On Convergence of the Empirical Spectral Distribution Function for a Special Type of Random Matrices to the Normal Law
Let \( X_1, X_2, \ldots , X_n \) be independent random variables, and let \( \mathbf {E}^{(l)} \) for \( l=1, \ldots , n \) be symmetric deterministic matrices. We study matrices of the type \( \mathbf {W} = \sum _{l=1}^n X_l \mathbf {E}^{(l)} \). The convergence of empirical spectral distribution of \( \mathbf {W} \) to the normal law is established under certain conditions on matrices \( \mathbf {E}^{(l)} \). Applications include estimating the convergence rate for the spectral distribution functions of palindromic and circulant random matrices. The analysis employs a method introduced by the author in his 1980 work “On the Rate of Convergence in the Central Limit Theorem for Weakly Dependent Variables”.- 22 December 2025
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
- Vol. 35 (4) , 343-355
On Convergence of the Empirical Spectral Distribution Function for a Special Type of Random Matrices to the Normal Law
Let \( X_1, X_2, \ldots , X_n \) be independent random variables, and let \( \mathbf {E}^{(l)} \) for \( l=1, \ldots , n \) be symmetric deterministic matrices. We study matrices of the type \( \mathbf {W} = \sum _{l=1}^n X_l \mathbf {E}^{(l)} \). The convergence of empirical spectral distribution of \( \mathbf {W} \) to the normal law is established under certain conditions on matrices \( \mathbf {E}^{(l)} \). Applications include estimating the convergence rate for the spectral distribution functions of palindromic and circulant random matrices. The analysis employs a method introduced by the author in his 1980 work “On the Rate of Convergence in the Central Limit Theorem for Weakly Dependent Variables”.- Open Access
- 20 June 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (13) , 2056
On the Limiting Distribution of the Spectra of Random Block Matrices
The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the universality of the limiting empirical distribution function of block-type random matrices is shown.
- 20 June 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (13) , 2056
Open AccessOn the Limiting Distribution of the Spectra of Random Block Matrices
The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the universality of the limiting empirical distribution function of block-type random matrices is shown.
- 23 December 2024
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 286 (5) , 668-683
Local Laws for Sparse Sample Covariance Matrices Without the Truncation Condition
- 23 December 2024
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 286 (5) , 668-683
Local Laws for Sparse Sample Covariance Matrices Without the Truncation Condition
- Open Access
- 22 July 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (14) , 2291
Limit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks
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.
- 22 July 2024
- Published by MDPI AG in Mathematics
- Vol. 12 (14) , 2291
Open AccessLimit Theorems for Spectra of Circulant Block Matrices with Large Random Blocks
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.
- Open Access
- 31 May 2024
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
- Vol. 34 (2) , 146-153
Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
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.
- 31 May 2024
- Published by Pleiades Publishing Ltd in Siberian Advances in Mathematics
- Vol. 34 (2) , 146-153
Open AccessMarchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
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.
- Open Access
- 25 August 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (17) , 3665
On the Special Issue “Limit Theorems of Probability Theory”
- 25 August 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (17) , 3665
Open AccessOn the Special Issue “Limit Theorems of Probability Theory”
- 17 July 2023
- Published by Springer Nature
- p. 261-300
Rate of Convergence for Sparse Sample Covariance Matrices
- 17 July 2023
- Published by Springer Nature
- p. 261-300
Rate of Convergence for Sparse Sample Covariance Matrices
- Open Access
- 2 February 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (3) , 764
Limit Theorem for Spectra of Laplace Matrix of Random Graphs
We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law and the normal law.
- 2 February 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (3) , 764
Open AccessLimit Theorem for Spectra of Laplace Matrix of Random Graphs
We consider the limit of the empirical spectral distribution of Laplace matrices of generalized random graphs. Applying the Stieltjes transform method, we prove under general conditions that the limit spectral distribution of Laplace matrices converges to the free convolution of the semicircular law and the normal law.
- Open Access
- 1 January 2023
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 28 (none) , 1-18
On the largest and the smallest singular value of sparse rectangular random matrices
We derive estimates for the largest and smallest singular values of sparse rectangular N×n random matrices, assuming limN,n→∞n N=y∈(0,1). We consider a model with sparsity parameter pN such that NpN∼logαN for some α>1, and assume that the moments of the matrix elements satisfy the condition E|Xjk|4+δ≤C<∞. We assume also that the entries of matrices we consider are truncated at the level (NpN)1 2−ϰ with ϰ:=δ 2(4+δ).
- 1 January 2023
- Published by Institute of Mathematical Statistics in Electronic Journal of Probability
- Vol. 28 (none) , 1-18
Open AccessOn the largest and the smallest singular value of sparse rectangular random matrices
We derive estimates for the largest and smallest singular values of sparse rectangular N×n random matrices, assuming limN,n→∞n N=y∈(0,1). We consider a model with sparsity parameter pN such that NpN∼logαN for some α>1, and assume that the moments of the matrix elements satisfy the condition E|Xjk|4+δ≤C<∞. We assume also that the entries of matrices we consider are truncated at the level (NpN)1 2−ϰ with ϰ:=δ 2(4+δ).
- Open Access
On the Largest and the Smallest Singular Value of Sparse Rectangular Random Matrices
We derive estimates for the largest and smallest singular values of sparse rectangular $N\times n$ random matrices, assuming $\lim_{N,n\to\infty}\frac nN=y\in(0,1)$. We consider a model with sparsity parameter $p_N$ such that $Np_N\sim \log^{\alpha }N$ for some $\alpha>1$, and assume that the moments of the matrix elements satisfy the condition $\mathbf E|X_{jk}|^{4+\delta}\le C<\infty$. We assume also that the entries of matrices we consider are truncated at the level $(Np_N)^{\frac12-\varkappa}$ with $\varkappa:=\frac{\delta}{2(4+\delta)}$.Open AccessOn the Largest and the Smallest Singular Value of Sparse Rectangular Random Matrices
We derive estimates for the largest and smallest singular values of sparse rectangular $N\times n$ random matrices, assuming $\lim_{N,n\to\infty}\frac nN=y\in(0,1)$. We consider a model with sparsity parameter $p_N$ such that $Np_N\sim \log^{\alpha }N$ for some $\alpha>1$, and assume that the moments of the matrix elements satisfy the condition $\mathbf E|X_{jk}|^{4+\delta}\le C<\infty$. We assume also that the entries of matrices we consider are truncated at the level $(Np_N)^{\frac12-\varkappa}$ with $\varkappa:=\frac{\delta}{2(4+\delta)}$.