Mariya Shcherbina
 Curriculum vitae

Publications

Publications in random matrix theory:
  1. A.Boutet de Monvel, and M.Shcherbina. On the norm of random matrices. Mat.Zametki, 57, N5, p.688-698 (1995) (Preprint University Paris-VII, 1992) (.pdf)
  2. L.Pastur, M.Shcherbina. Eigenvalue distribution for a certain class of random matrices in the limit of their infinite order. Math. Phys., Anal., Geom., 1, 131-138 (1994)
  3. A.Boutet de Monvel, L.Pastur and M.Shcherbina. On the statistical mechanics approach in the Random Matrix Theory. Integrated Density of States. J.Stat.Phys., 79, p.585-611 (1995)
  4. L.Pastur, M.Shcherbina. Universality of the Local Eigenvalue Statistics for a Class of Unitary Invariant Matrix Ensembles. J.Stat.Phys., 86, p.109-147 (1997 )(Preprint IMA N1315, Minneapolis, 1995) (.pdf)
  5. S.Albeverio, L.Pastur and M.Shcherbina. On Asymptotic Properties of Certain Ortogonal Polynomials. Matem. Fiz., Analiz, Geom., 4, N3, p.263-277 (1997) (.pdf)
  6. S.Albeverio, L.Pastur and M.Shcherbina. On the 1/n expansion for some unitary invariant ensembles of random matrices. Commun.Math.Phys. 224, p.271-305, (2001) (.pdf)
  7. A.Boutet de Monvel, M. Shcherbina. On the Free Energy of the Two Dimensional U(n)-Gauge Field Theory on the Sphere. Teor.Mat.Fiz. 115, N3, p.389-401 (1998) (.pdf)
  8. A.Boutet de Monvel, M.Shcherbina, D.Shepelsky. On the integrated density of states for a certain ensemble of random matrices. Random Oper. Stoch. Eqs., 6, N4, p.331-338 (1998)
  9. L.Pastur, M.Shcherbina. On the ege universality of the local eigenvalue statistics of matrix models. Matematicheskaya fizika, analiz, geometriya, 10, N3, 335-365 (2003) (.pdf)
  10. O.Khorunzhy, M.Shcherbina, V.Vengerovsky. Eigenvalue distribution of large weighted random graphs. Journal of Mathematical Physics, 45, N. 4, 1648-1672 (2004) (.pdf)
  11. L.Pastur, M.Shcherbina. Bulk universality and related properties of the unitary. Journal of Statistical Physics, 130, no. 2, pp. 205-250, (2007) (.pdf)
  12. M.Shcherbina. Central limit theorem for linear eigenvalue statistics of orthogonally invariant matrix models Journal of Mathematical Physics, Analysis, Geometry 4, N1 pp.171-195, 2008 (.pdf)
  13. J.Feng, M.Shcherbina, B.Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure and Applied Analysis 7, p. 249-265,( 2008)
  14. M.Shcherbina. Double scaling limit for matrix models with non analytic potentials. J. Math. Phys. 49, n3 pp. 033501-033535, (2008) (.pdf)
  15. M.Shcherbina. On Universality for Orthogonal Ensembles of Random Matrices Commun.Math.Phys. 285, pp 957-974, (2009)  (.pdf)
  16. M.Shcherbina. Edge Universality for Orthogonal Ensembles of Random Matrices. Journal of Statistical Physics: 136, N1, pp 35-50, (2009)  (.pdf)
  17. M.Shcherbina, B.Tirozzi. Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs J. Math. Phys 51, N2 (2010)  (.pdf)
  18. M.Shcherbina. Orthogonal and symplectic matrix models: universality and other properties Preprint arXiv:math-ph/1003.6121 Commun.Math.Phys. 307, Issue 3 pp 761-790, 2011; DOI: 10.1007/s00220-011-1351-5.
  19. L.Pastur, M.Shcherbina. Eigenvalue Distribution of Large Random Matrices. Mathematical Survives and Monographs, V171, American Mathematical Society: Providence, Rhode Island (2011)
  20. M.Shcherbina. Central Limit Theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices. Journal of Mathematical Physics, Analysis, Geometry V7, N2, pp 176-192, 2011.
  21. M.Shcherbina, B.Tirozzi. Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime. arXiv:1111.5492[math-ph]. J.Math.Phys. Vol.53, Issue 4, 043501 (1-18) (2012) DOI: 10.1063/1.3698291
  22. M.Shcherbina, B.Tirozzi. Quantum Hopfield model. arXiv:1201.5024[math-ph].
  23. M.Shcherbina. Fluctuations of linear eigenvalue statistics of β matrix models in the multicut regime arXiv:1205.7062[math-ph] J.Stat.Phys. DOI 10.1007/s10955-013-0740-x, V 151, N 6 (2013), 1004-1034
  24. A.Bufetov, S.Mkrtchyan, M.Shcherbina, A.Soshnikov. Entropy and the Shannon-McMillan-Breiman theorem for beta random matrix ensembles. J Stat Phys V152 (2013), 1-14 DOI 10.1007/s10955-013-0761-5
  25. M.Shcherbina. Change of variables as a method to study general β-models: bulk universality arXiv:1310.7835[math-ph] J. Math. Phys. Vol 55, N4, 043504 (2014) DOI: 10.1063/1.4870603
  26. M.Shcherbina. Asymptotic expansions for β matrix models and their applications to the universality conjecture in:Random Matrix Theory, Interacting Particle Systems and Integrable Systems. (Percy Deift and Piter Forrester Eds) Cambridge University Press 2014 ISBN: 9781107079922
  27. M.Shcherbina. On fluctuations of eigenvalues of random band matrices, arXiv:1504.05762 J Stat Phys, DOI 10.1007/s10955 J.Stat.Phys., Vol 161, Issue 1, pp 73-90 (2015)
  28. M.Shcherbina. Fluctuations of the eigenvalue number in the fixed interval for β-models with β = 1,2,4 arXiv:1504.05758 Theory and Applications in Mathematical Physics, 2015, pp. 131-146 ISBN: 978-981-4713-27-6 World Scientfic Publishing Co. Pte. Ltd. Singapore 596224
  29. A.Elgart, L.Pastur, M. Shcherbina. Large block properties of the entanglement entropy of disordered fermions. arXiv:1601.00294 (quant-ph) J Stat Phys (2017) 166:1092-1127 DOI 10.1007/s10955-016-1656-z
  30. M. Shcherbina, T. Shcherbina. Characteristic polynomials for 1D random band matrices from the localization side. arXiv:1602.08737 Com.Math.Phys. V 351, Issue 3, pp 1009-1044 (2017) DOI 10.1007/s00220-017-2849-2
  31. M. Shcherbina, T. Shcherbina. Transfer matrix approach to 1d random band matrices: density of states arXiv:1603.08476 J Stat Phys 164(6), 1233-1260 (2016). doi:10.1007/s10955-016-1593-x
  32. M. Shcherbina, T. Shcherbina. Universality for 1d Random Band Matrices: Sigma-Model Approximation J Stat Phys, 172(2), 627-664, DOI 10.1007/s10955-018-1969-1
  33. M. Shcherbina, T. Shcherbina. Transfer matrix approach to 1d random band matrices Proc. Int. Cong. of Math. 2018 Rio de Janeiro, Vol. 2 (2673-2694)
  34. L.Pastur, M.Shcherbina. Szego-type Theorems for One-Dimensional Schrodinger Operator with Random Potential (Smooth Case) arXiv:1809.04813 Zh. Mat. Fiz. Anal. Geom. Vol. 3(2018),1-27
Publications in spin glasses and neural networks theory:
  1.  L.A. Pastur, M.V. Shcherbina Long-range limit for the correlation function of the lattice systems. Teor. Mat. Fiz. , 61 , N1 (1984)
  2. M.V. Shcherbina Long-range limit for the correlation functions of the classical continuos systems for small activities. Dokl. Ac. Sci.Ukr SSR, A , p.5, (1985)
  3. M.Shcherbina. Classical Heisenberg model at zero temperature. Teor.Mat.Fiz. 81, N1, p.134-144 (1989)
  4. B.Khoruzhenko, L.Pastur, and M.Shcherbina. Generalized spherical model in an inhomogeneous field Preprint, Inst. for Low Temp. Phys. Engin. 1987, N41-87, pp 1-43.
  5. B.Khoruzhenko, L.Pastur, and M.Shcherbina. On the critical temperature of the Heisenberg model's spherical limit on a decorated lattice Preprint, Inst. for Low Temp. Phys. Engin. 1988, N22-88, pp 1-10.
  6. M.Shcherbina. Spherical limit of n-vector correlations. Teor.Mat.Fiz. 77 , N3, p.460-471 (1988)
  7. B.Khoruzhenko, L.Pastur, and M.Shcherbina. Large-n limit of the Heisenberg model: the decorated lattice and the disordered chain. J.Stat.Phys. 57 , 41-52 (1989)
  8. H.Englisch, A.Engel, A.Schutte, and M.Shcherbina. Strongly diluted networks with retrieval-dependent threshholds. In: Computer Analysis of Images and Patterns (Eds.: K.Voss, D.Chetvericov, Sommer) Akademievelag Berlin , p.95-103 (1989)
  9. B.Khoruzhenko, M.Shcherbina, and V.Slusarev. On a magnetic model for doped CuO systems. Preprint Karl-Marx-Universitat, Leipzig , 1990.
  10. H.Englisch, A.Engel, A.Schutte, and M.Shcherbina. Improved retrieval in nets of formal neurons with thressholds and non linear synapses. Studia Biophisica. p.136, 1990.
  11. L.Pastur, and M.Shcherbina. The absence of the selfaverageness of the order parameter in the Sherrington-Kirkpatrick model. J.Stat.Phys., 62, N1/2, p.1-19 (1991)
  12. M.Shcherbina. The infinite component limit for Hopfield model. Teor.oper., Kiev :Naukova dumka, p.164-172 (1991) (in russian)
  13. M.Shcherbina. More about the absence of selfaverageness of order parameter in SK-model. Preprint Rome University -I, 1991.
  14. A.Khorunzy, B.Khoruzhenko, L.Pastur and M.Shcherbina. The Large-n limit in statistical mechanics and spectral theory of disordered systems. Phase transition and critical phenomena. v.15 , p.73, Academic Press , 1992.
  15. Khoruzhenko B., Pastur L., Shcherbina M. The Infinite Component Limit of the random Anisotrophy n-Vector Model, Adv. in Sov. Math., 19 , p.269-286 (1994)
  16. M.Shcherbina and B.Tirozzi. The free energy of the class of Hopfield model JSP. 72 , p.113-125 (1993)
  17. L.Pastur M.Shcherbina and B.Tirozzi. The Hopfield model without replica trick. JSP, 4 , p.1161-1183 (1994)
  18. M. Shcherbina, B. Tirozzi, Saddle Point Equations of a Neural Network with Correlated Attractors. J. de Physique I 4, p. 629-633, (1994)
  19. M. Shcherbina. Tirozzi B. A Perturbative Expansion for the Hopfield Model, Helvetica Physica Acta, 69 , N5, p.470 (1995)
  20. M. Shcherbina. On the Replica Symmetric Solution for the Sherrington-Kirkpatrick Model . HPA, 70 , p.838-853 (1997)(.pdf) 
  21. M.Shcherbina,. Some estimates for the critical temperature of the Sherrington-Kirkpatrick model with magnetic field. In: Mathematical Results in Statistical Mechanics. World Scientific, Singapure, p.455-474, 1999. (.pdf) .
  22. L.Pastur, M.Shcherbina, B.Tirozzi. On the replica symmetric equations for the Hopfield model. J.Math.Phys. 40 (1999) (.pdf)
  23. J.Feng, M.Shcherbina, B.Tirozzi . On the critical capacity of the Hopfield model. Commun.Math.Phys. 216, p.139-177, (2001) (.pdf)
  24. M.Shcherbina, B.Tirozzi. Generalization and learning error for non linear perceptron. Mathematical and Computing Modelling 35 , p.259-271 (2002) (.pdf)
  25. M.Shcherbina, B.Tirozzi.Rigorous Solution of the Gardner Problem Preprint ArXiv math-ph/0112003 (2001), Rigorous Solution of the Gardner Problem. Commun.Math.Phys, 234 , p.383-422 (2003) (.pdf)
  26. M.Shcherbina, B.Tirozzi.On the Volume of the Intersection of a Sphere with Random Half Spaces. CRAS Ser.I 334 p.803-806, (2002) (.pdf)
  27. M.Shcherbina, B.Tirozzi. Convexity and Intersection of Random Spaces. Proceedings of China Japanese Seminar Re-finements of number –theoretic methods (2002) (.pdf)
  28. M.Shcherbina, B.Tirozzi. Central Limit Theorems for Order Parameters of the Gardner Problem, Markov processes and related fields, N4, p.583-602 (2003) (Preprint ArXiv cond-mat/ (2002)) (.pdf)
  29. M.Shcherbina, B.Tirozzi. Stability of asynchronous states of spiking neurons. International Journal of Modern Physics B, 18, N 4 - 5, 759-771 (2004) (.pdf)
  30. M.Shcherbina, B.Tirozzi.Central limit theorems for the free energy of the modified Gardner problem. Markov processes and related fields, N 1, p.1-17 (2005) (.pdf)
  31. M.Shcherbina. Some mathematical problems of neural networks theory. In: Proceedings of the 4th Europian Congress in Mathematics. EMS Publishing house, 2005(.pdf)
  32. J.Feng, M.Shcherbina, B.Tirozzi, G.O.You. Optimal movement control models of Langeven and Hamiltonian types. Mathematical and computer modelling 46 , p.680-698, (2007) (.pdf) 
  33. J.Feng, M.Shcherbina, B.Tirozzi. Stability of the dynamics of an asymmetric neural network Communications on Pure and Applied Analysis 8 , p.655-671, 2009 (.pdf)