Research Papers


Fluctuations of Matrix Entries of Regular Functions of Sample Covariance Random Matrices
available at arXiv:1106.0320 math.PR
(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
to appear in the Journal of Theoretical Probability
(joint with Sean O'Rourke and David Renfrew).


On Finite Rank Deformations of Wigner Matrices
available at arXiv:1103.3731 math.PR
to appear in the Annales de l'Institut Henri Poincare (B) Probabilites et Statistiques
(joint with Alessandro Pizzo and David Renfrew).


Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices
available at arXiv:1103.1170 math.PR
to appear in the Journal of Statistical Physics
(joint with Alessandro Pizzo and David 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 ).


Here is also a link to the paper Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices by my former Ph.D. student Sean O'Rourke .
The paper is published in J. Stat. Phys. v. 138 pp. 1045-1066 (2010).


Spectral Properties of Large Random Matrices with Independent Entries
to appear in the peer-reviewed Proceedings of the XIIIth Workshop "Noncommutative Harmonic Analysis" (Bedlewo, Poland, 2010), Banach Center Publications (M.Bozejko, A.Krystek, L.Wojakowski eds.)
(joint with P. Dueck, S. O'Rourke and D. Renfrew)


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)