Mariya Shcherbina
Curriculum vitae
Publications
Publications in random matrix theory:
- 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)
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- 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)
- 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)
- 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)
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- S.Albeverio, L.Pastur and M.Shcherbina. On Asymptotic Properties of Certain Ortogonal Polynomials. Matem. Fiz., Analiz, Geom., 4, N3, p.263-277 (1997)
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- 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)
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- 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)
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- 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)
- 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)
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- O.Khorunzhy, M.Shcherbina, V.Vengerovsky. Eigenvalue distribution of large weighted random graphs.
Journal of Mathematical Physics, 45 , N. 4, 1648-1672 (2004)
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- L.Pastur, M.Shcherbina Bulk universality and related properties of the unitary.
Journal of Statistical Physics, 130 , no. 2, pp. 205-250, (2007)
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- 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
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- J.Feng, M.Shcherbina, B.Tirozzi. Dynamical behaviour of a large complex system.
Communications on Pure and Applied Analysis 7 , p. 249-265,( 2008)
- M.Shcherbina. Double scaling limit for matrix models with non analytic potentials. J. Math. Phys. 49, n3 pp. 033501-033535, (2008)
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- M.Shcherbina. On Universality for Orthogonal Ensembles of Random Matrices Commun.Math.Phys. 285, pp 957-974, (2009)
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- M.Shcherbina. Edge Universality for Orthogonal Ensembles of Random Matrices. Journal of Statistical Physics: 136, N1, pp 35-50, (2009)
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- M.Shcherbina, B.Tirozzi Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
J. Math. Phys 51 , N2 (2010)
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Publications in spin glasses and neural networks theory :
- L.A. Pastur, M.V. Shcherbina Long-range limit for the correlation function of the lattice systems. Teor. Mat. Fiz. ,
61 , N1 (1984)
- 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)
- M.Shcherbina. Classical Heisenberg model at zero temperature. Teor.Mat.Fiz.
81, N1, p.134-144 (1989)
- 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.
- 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.
- M.Shcherbina. Spherical limit of n-vector correlations. Teor.Mat.Fiz.
77 , N3, p.460-471 (1988)
- 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)
- 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)
- B.Khoruzhenko, M.Shcherbina, and V.Slusarev. On a magnetic model for doped CuO systems. Preprint Karl-Marx-Universitat, Leipzig , 1990.
- 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.
- 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)
- M.Shcherbina. The infinite component limit for Hopfield model.
Teor.oper., Kiev :Naukova dumka, p.164-172 (1991) (in russian)
- M.Shcherbina. More about the absence of selfaverageness of order parameter in SK-model. Preprint Rome University -I, 1991.
- 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.
- 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)
- M.Shcherbina and B.Tirozzi. The free energy of the class of Hopfield model JSP.
72 , p.113-125 (1993)
- L.Pastur M.Shcherbina and B.Tirozzi. The Hopfield model without replica trick. JSP,
4 , p.1161-1183 (1994)
- M. Shcherbina, B. Tirozzi, Saddle Point Equations of a Neural Network with Correlated Attractors. J. de Physique I
4, p. 629-633, (1994)
- M. Shcherbina. Tirozzi B. A Perturbative Expansion for the Hopfield Model, Helvetica Physica Acta,
69 , N5, p.470 (1995)
- M. Shcherbina. On the Replica Symmetric Solution for the Sherrington-Kirkpatrick Model . HPA,
70 , p.838-853 (1997)(.pdf)
- 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.
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- L.Pastur, M.Shcherbina, B.Tirozzi. On the replica symmetric equations for the Hopfield model. J.Math.Phys.
40 (1999) (.pdf)
- J.Feng, M.Shcherbina, B.Tirozzi . On the critical capacity of the Hopfield model.
Commun.Math.Phys.
216, p.139-177, (2001) (.pdf)
- M.Shcherbina, B.Tirozzi. Generalization and learning error for non linear perceptron.
Mathematical and Computing Modelling
35 , p.259-271 (2002) (.pdf)
- 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)
- 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)
- M.Shcherbina, B.Tirozzi. Convexity and Intersection of Random Spaces. Proceedings of China Japanese Seminar Re-finements of number –theoretic methods (2002)
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- 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))
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- 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)
- 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)
- M.Shcherbina. Some mathematical problems of neural networks theory. In: Proceedings of the 4th Europian
Congress in Mathematics. EMS Publishing house, 2005(.pdf)
- 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)
- 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)
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