Zobrazeno 1 - 10
of 121
pro vyhledávání: '"Soshnikov, Alexander"'
Autor:
Soshnikov, Alexander
Motivated by the Rudnick-Sarnak theorem we study limiting distribution of smoothed local correlations of the form $$ \sum_{j_1, j_2, \ldots, j_n} f(N\*(\theta_{j_2}-\theta_{j_1}), N\*(\theta_{j_3}-\theta_{j_1}), \ldots, N\*(\theta_{j_n}-\theta_{j_1})
Externí odkaz:
http://arxiv.org/abs/2207.00674
Autor:
Aguirre, Ander, Soshnikov, Alexander
We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i\neq j}f(L_N(\theta_i-\theta_j))$ for arbitrary $\beta>0$ in the mesoscopic regime $L_N=O(N^{2/3-\epsilon})$.
Comment: added results on
Comment: added results on
Externí odkaz:
http://arxiv.org/abs/2109.13339
Autor:
Aguirre, Ander, Soshnikov, Alexander
We prove Gaussian fluctuation for pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(\theta_i-\theta_j)$ for the Circular Unitary Ensemble (CUE) of random matrices in the case of a slowly growing variance in the limit of large $N.$
Externí odkaz:
http://arxiv.org/abs/2004.01345
We study limiting distribution of pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(L_N\*(\theta_i-\theta_j))$ for the circular $\beta$-ensemble (C$\beta$E) of random matrices for sufficiently smooth test function $f$ and $L_N=O(N).
Externí odkaz:
http://arxiv.org/abs/1912.07110
Autor:
Soshnikov, Alexander, Xu, Yuanyuan
In this paper, we consider a strongly-repelling model of $n$ ordered particles $\{e^{i \theta_j}\}_{j=0}^{n-1}$ with the density $p({\theta_0},\cdots, \theta_{n-1})=\frac{1}{Z_n} \exp \left\{-\frac{\beta}{2}\sum_{j \neq k} \sin^{-2} \left( \frac{\the
Externí odkaz:
http://arxiv.org/abs/1710.11328
Autor:
Jana, Indrajit, Soshnikov, Alexander
We consider the limiting spectral distribution of matrices of the form $\frac{1}{2b_{n}+1} (R + X)(R + X)^{*}$, where $X$ is an $n\times n$ band matrix of bandwidth $b_{n}$ and $R$ is a non random band matrix of bandwidth $b_{n}$. We show that the St
Externí odkaz:
http://arxiv.org/abs/1610.02153
We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic covariance to a fam
Externí odkaz:
http://arxiv.org/abs/1504.05933
Autor:
Soshnikov, Alexander1 (AUTHOR) soshniko@math.ucdavis.edu, Wu, Chutong1 (AUTHOR)
Publikováno v:
Entropy. May2023, Vol. 25 Issue 5, p725. 16p.
In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\frac{1}{\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the diagonal eleme
Externí odkaz:
http://arxiv.org/abs/1412.2445
Publikováno v:
J. Stat. Phys. Vol. 160, No. 1 (2015), 89--119
For fixed $m > 1$, we study the product of $m$ independent $N \times N$ elliptic random matrices as $N$ tends to infinity. Our main result shows that the empirical spectral distribution of the product converges, with probability $1$, to the $m$-th po
Externí odkaz:
http://arxiv.org/abs/1403.6080