Research Papers


Gaussian Fluctuation for Smoothed Local Correlations in CUE
Journal of Statistical Physics vol. 190 (2023)

Central Limit Theorem for C\Beta E Pair Dependent Statistics in Mesoscopic Regime
Electronic Communications in Probability, no. 38, 1-10, (2022)
(joint with Ander Aguirre)

Pair Dependent Linear Statistics for Circular Beta Ensemble
available at arXiv:1912.07110 math.PR
Random Matrices: Theory and Applications vol. 10, No. 4, 2150035, (2021)
(joint with Ander Aguirre and Joshua Sumpter)

A NOTE ON PAIR DEPENDENT LINEAR STATISTICS WITH SLOWLY GROWING VARIANCE
available at arXiv:2004.01345 math.PR
Theoretical and Mathematical Physics, vol. 205, No. 3, 502-512, (2020)
(joint with Ander Aguirre)

Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle.
Theory of Probablity and Its Applications vol. 65 No. 4 (2020).
(joint with Yuanyuan Xu)

Central Limit Theorem for Linear Eigenvalue Statistics for Submatrices of Wigner Random Matrices
Frontiers in Applied Mathematics and Statistics, section Mathematical Physics, 6:17, (2020).
(joint with Lingyun Li and Matthew Reed)

Distribution of Singular Values of Random Band Matrices: Marchenko-Pastur Law and More
Journal of Statistical Physics. vol. 168 No.5, 964-985, (2017).
(joint with Indrajit Jana)

Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices
Theory of Probablity and Applications Vol. 60, No. 3, 407-443, (2016).
(joint with Indrajit Jana and Koushik Saha)

Products of independent elliptic random matrices
available at arXiv:1403.6080 math.PR
Journal of Statistical Physics Vol. 160, No. 1 (2015), 89--119.
(joint with Sean O'Rourke, David Renfrew, and Van Vu

Partial Linear Eigenvalue Statistics for Wigner and Sample Covariance Random Matrices
available at arXiv:1301.0368 math.PR
Journal of Theoretical Probability v. 28, (2015), 726-744.
(joint with Sean O'Rourke)

Central Limit Theorem for Linear Statistics of Eigenvalues of Band Random Matrices
available at arXiv:1304.6744 math.PR
Random Matrices: Theory and Applications, v. 2, No. 4, (2013) 1350009, 50 pages
(joint with Lingyun Li)

Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles
available at arXiv:1301.0342 math.PR
Journal of Statistical Physics, v. 152, No. 1 (2013), 1-14.
(joint with Alexander Bufetov, Sevak Mkrtchyan, and Maria Shcherbina)

On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations
available at arXiv:1203.5130 math.PR
Random Matrices: Theory and Applications, v. 2, No. 1 (2013).
(joint with David Renfrew).


Fluctuations of Matrix Entries of Regular Functions of Sample Covariance Random Matrices
available at arXiv:1106.0320 math.PR
Theory of Probability and its Applications v. 58, No. 4 (2013), 752-780.
(joint with Sean O'Rourke and David Renfrew).


On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries
available at arXiv:1104.1663 math.PR
Journal of Theoretical Probability v. 26, No. 3, (2013), 750-780.
(joint with Sean O'Rourke and David Renfrew).


On Finite Rank Deformations of Wigner Matrices
available at arXiv:1103.3731 math.PR
Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques, v.49, No. 1, 64-94, (2013).
(joint with Alessandro Pizzo and David Renfrew).


Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices
available at arXiv:1103.1170 math.PR
Journal of Statistical Physics, v. 146, No. 3, 550-591, (2012).
(joint with Alessandro Pizzo and David Renfrew).


Spectral Properties of Large Random Matrices with Independent Entries
Noncommutative Harmonic Analysis with Applications to Probability III. Banach Center Publications vol. 96, 115-134 (2012)
(joint with P. Dueck, S. O'Rourke and D. Renfrew)


Products of Independent Non-Hermitian Random Matrices
available at arXiv:1012.4497 math.PR
Electronic Journal of Probability, No. 81, 2219-2245, (2011).
(joint with Sean O'Rourke ).


On the Resolvent Identities in Gaussian Ensembles at the Edge of the Spectrum
New Trends in Mathematical Physics, 615-627, (2009).


On the Lower Bound of the Spectral Norm of Symmetric Random Matrices with Independent Entries
Elec. Commun. Probab. vol. 13, 280-290, (2008).
(joint with Sandrine Peche ).


Wigner Random Matrices with Non-symmetrically Distributed Entries
J. Stat. Phys. , vol. 129, No. 5/6, 857-884, (2007).
(joint with Sandrine Peche ).


Determinantal Random Fields
Encyclopedia of Mathematical Physics, (eds. Jean-Pierre Francoise, Greg Naber and Tsou Sheung Tsun).
Oxford: Elsevier, 2006, v.2, pp. 47-53.


Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensembles
Lect. Notes Phys. 690, 351-364, (2006).


Statistics of Extreme Spacings in Determinantal Random Point Processes
Moscow Math. J., vol. 5, No.3, 705-719, (2005).


On the Largest Singular Values of Random Matrices with Independent Cauchy Entries
J. Math. Phys., 46, 033302 (2005), 15 pages,
(joint with Yan Fyodorov ).


Poisson Statistics for the Largest Eignevalues of Wigner Random matrices with Heavy Tails
Elec. Commun. Probab., 9 (2004), 82-91.


Janossy Densities of Coupled Random Matrices
Commun. Math. Phys., vol. 251, pp.447-471, (2004).


Janossy Densities I. Determinantal Ensembles
J.Stat.Phys., vol. 113, Nos. 3/4, pp. 595-610, (2003).
(joint with Alexei Borodin ).


Janossy Densities II. Pfaffian Ensembles
J.Stat.Phys., vol. 113, Nos. 3/4, pp. 611-622, (2003).


On the Largest Eigenvalue of a Random Subgraph of the Hypercube
Commun. Math. Phys. vol. 239, pp. 53-63, (2003), arXiv preprint math.PR/0209178
(joint with Benny Sudakov ).


Gaussian Limit for Determinantal Random point Fields
Annals of Probability, v.30, No.1, pp.171-187, (2002)


A Note on Universality of the Distribution of the Largest Eigenvalues in Certain Sample Covariance Matrices
J. Stat. Phys., v.108, Nos. 5/6, pp. 1033-1056, (2002)


Random Matrices and Quantum Chaos
Proceedings of the National Academy of Sciences USA, vol. 98, No. 19, pp 10531-10532, (2001)
(joint with T.Kriecherbauer and J.Marklof )


Central Limit Theorem for Linear Statistics in Classical Compact Groups and Related Combinatorial Identities
Annals of Probability, v. 28, pp. 1353-1370, (2000)


Determinantal Random Point Fields
Russian Mathematical Surveys, vol.55, No.5, pp.923-975, (2000)
and here is the Russian version of the same paper in Uspekhi Matematicheskikh Nauk


Gaussian Fluctuation of the Number of Particles in Airy, Bessel, sine and Other Determinantal Random point Fields
J. Stat. Phys., v.100, Nos. 3/4, pp. 491-522, (2000)


Universality at the Edge of the Spectrum in Wigner Random Matrices
Commun. Math. Phys., v.207, pp.697-733, (1999)


Level spacings Distribution for Large Random Matrices: Gaussian Fluctuations
Annals of Mathematics, vol. 148, pp.573-617, (1998)


A Refinement of Wigner's Semicircle Law in a Neighborhood of the Spectrum edge
Functional Analysis and its Applications, vol. 32, No.2, pp.114-131, (1998)
(joint with Ya.Sinai)
and here is the Russian version of the same paper


Central Limit Theorem for the Traces of High Powers of Large Random Matrices with Independent Components
Bol. Soc. Bras. Mat vol. 29, No. 1, pp. 1-24, (1998) (volume dedicated to the memory of Ricardo Mane)
(joint with Ya.Sinai)


Splitting of the Low Landau Levels into a Set of Positive Lebesgue Measure under Small Periodic Perturbations
Commun. Math. Phys, vol. 189, pp.559-575, (1997)
(joint with E.I.Dinaburg and Ya.Sinai)


Difference Almost-Periodic Schrodinger Operators : Corollaries of Localization.
Commun. Math. Phys. vol. 153, pp.465-477, (1993)