A. Soshnikov

activity

19992022

most citedDeterminantal random point fields

382 citations · 907 across the 35 of their papers we have counts for

collaborators

35 papers

math.PR2022

Gaussian Fluctuation for Smoothed Local Correlations in CUE

Alexander Soshnikov

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\*(θ_{j_2}-θ_{j_1}), N\*(θ_{j_3…

math.PR2021

Central Limit Theorem for $C β E$ Pair Dependent Statistics in Mesoscopic Regime

Ander Aguirre, Alexander Soshnikov

We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i \neq = j} f (L_{N} (θ_{i} - θ_{j}))$ for arbitrary $β > 0$ in the mesoscopic regime $…

math.PR2020★ 3 cited

A note on pair dependent linear statistics with slowly growing variance

Ander Aguirre, Alexander Soshnikov

We prove Gaussian fluctuation for pair counting statistics of the form $\sum_{1 \leq i \neq = j \leq N} f (θ_{i} - θ_{j})$ for the Circular Unitary Ensemble (CUE) of random matrices in the ca…

math.PR2019★ 1 cited

Pair Dependent Linear Statistics for Circular Beta Ensemble

Ander Aguirre, Alexander Soshnikov, Joshua Sumpter

We study limiting distribution of pair counting statistics of the form $ \sum_{1\leq i\neq j\leq N} f(L_N\*(θ_i-θ_j))$ for the circular $β$ -ensemble (C $β$ E) of random matrices for…

math.PR2016★ 3 cited

Distribution of singular values of random band matrices; Marchenko-Pastur law and more

Indrajit Jana, Alexander Soshnikov

We consider the limiting spectral distribution of matrices of the form $\frac{1}{2 b _{n} + 1} (R + X) (R + X)^{*}$ , where $X$ is an $n \times n$ band matrix of bandwidth $b_{n}$ and $R$ …

math.PR2015★ 1 cited

Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices

Lingyun Li, Matthew Reed, Alexander Soshnikov

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…