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SELECTED PUBLICATIONS:

There are more than 300 total number of scientific publications.� The list of principal works is given below, divided into sections according to subject.� The entire number of publications within each section is in parentheses.

Monographs and monographic reviews (6)

1.  "Ideas in the theory of Random Media," Acta. Appl. Math, 1991, 12, 139-282, Kluver Acad. Publish.
2. "Intermittency, diffusion and generation in a non-stationary Random Medium," Sov. Sci. Reviews, Sec. C, 7, 1-110, Harvard Acad. Publish. (with Ju. Zaldovich, A. Ruzmaikin, D. Sokolov).
3. "Lectures on probability theory," 1992 Summer School in Probability, Saint-Flour, France, ed. 1994, Springer-Verlag lecture notes, #1581.� (with D. Bakry, R. Gill).
4. "Parabolic Anderson model and intermittency," Memoirs of American Math. Soc., 518.� (with R. Carmona).
5. "Topics in statistical oceanography" (lectures), (1995 - preprint UNCC), Proceedings of the ONR-conferences (Santa Monica 1993, Santa Barbara 1994), Stochastic Modelling in Physical Oceanography," Birckhauser, 1996, 343-381.
6. "Multiscale averaging for ordinary differential equations.� Applications to the spectral theory of one-dimensional Schr�dinger operator with sparse potential", 1999.� In Homogenization, ed. V. Berdichersky, V. Jikov, G. Paparieolasu, World Scientific, Series in Math and Appl. vol 50, pp. 316-397.  

Research Articles

I.� Boundary Theory for Markov Processes (12)

1. "Some questions in the theory of Martin boundaries,"� Candidate thesis, 1967, 80 pp. (Russian).
2. "Martin boundary for invariant Markov processes on a solvable group,"� Teor. Veroyatnost. i Primenen., 1967, 12, No. 2, 5 pp.
3. "Martin boundary for a direct product of Markov processes," Sibirsk. Matem. Zurn., 1970, 11, No. 2, 12 pp.

II. Diffusion on Riemannian Manifolds and Classical Spectral Theory (15)

1. �Diffusion processes and Riemannian geometry," Uspekhi Mathem. Nauk, 1975, 30, No. ����������� 1, 57 pp.
2. Asymptotic formulas for transition density of the Wiener process in thin tubes,"� Demonstr. Math. (Poland), 1982, 15, No. 3, 20 pp. (with Yu. Sidorovich).
3. "Spectral invariants of the Schr�dinger operator on the Euclidian torus,"� Dokl. Sov. Acad. Sci., 1986, v. 286, w2, 5 pp. (with M. Novitzkii).
4. �Eigenvalue distribution of the Neuman Laplacian or regions and manifolds with gasps,"� ����������� J. Funct. Anal., 1992, v. 108, w. 1, 5 pp. (with B. Simon and V. Jaksic).

III.� Localization Theory (40)

1. "A random one-dimensional Schr�dinger operator has a pure point spectrum,"
2. Funckcional. Anal. i Prilozen, 1977, 11, No. 1, 10 pp. (with I. Goldsheid and L. Pastur).
3. "The structure of eigenfunctions of one-dimensional unordered structures," Izv. Akad. Nauk SSSR Ser. Mat., 1978, 42, No. 1, 34 pp.
4. The local structure of the spectrum of the one-dimensional Schr�dinger operator," Comm. Math. Phys., 1981, 78, No. 3, 17 pp.
5. "Spectral properties of the general Sturm-Liouville equation with random coefficients,"� Math. Nachr. (DDR), 1982, 102, 22 pp. (with H. Seidel).
6. "On the basic states of one-dimensional disordered structures,"� Comm. Math. Phys., 1983, 90, No. 1, 23 pp. (with L. Grenkova and L. Sudarev).
7. "Spectral properties of random operators," Doctor thesis, 1983, 300 pp.
8. "Spectral properties of rare scatterers and counterexamples to Schr�dinger and Steklov hypotheses," Proc. Math. Phys. Congress, England 1989, 15 pp. (with V. Maslov).
9. �One-dimensional Schr�dinger operator with unbounded potential:� pure point spectrum," Funct. Anal. and Appl., 1990, 3, 24 pp. (with L. Pastur, V. Kirsch).
10. "Lectures on localization theory," preprint, Caltech, 1990, 58 pp.
11. "Intermittency and localization:� new results,"� Thesis of ICM, Kyoto, Japan, 1990.
12. �Localization at large disorder and extreme energies:� an elementary derivation," Comm. ����������� Math. Phys., to appear, 1993, 50 pp.
13. "Spectral properties of random Schr�dinger operator with unbounded potentials, "Comm. Math. Phys., to appear, 1992, 40 pp.

IV.� Percolation Theory (18)

1. "Percolation theory and its applications," Itogi Nauki i Tekniki, 24, Moskva:� VINITI, 1986, 58 pp. (with M. Menshikov and A. Sidorenko).
2. "Percolation in random fields," I, II, III, Teoret. i Matem. Fiz., 1983, 55, No. 2, 11 pp., ����������� 1983, 55, No. 3, 12 pp., 1986, 67, No. 2, 9 pp. (with A. Stepanov).
3. "Multiscale failure and percolation models,"� PAGEOPH, 1990, W61, 10 pp. (with V. Pisarenko and A. Reznidova).

Averaging, Intermittency, and Diffusion in Random Media (60)

1. "Kinematic dynamo in random flow," Uspekhi Fiz. Nauk, 1985, 145, No. 4, 36 pp.
2. "Intermittency, diffusion and generation in a nonstationary random medium," Sov. Rev. in Math. Phys., Ser. C, v. 7, 1988, 7, 110 pp. (with Ja. Zeldovich, A. Ruzmaikin, D. Sokolev).
3. "Intermittency in a random medium," Uspekhi Fiz. Nauk, 1987, 152, No. 1, 30 pp. (with Ja. Zeldovich, A. Ruzmaikin, D. Sokolov).
4. "Ideas in the theory of random media," Manuscript of a book, deposed in VINITY, 1988, No. 9140B88, 176 pp. (Russian).
5. "Ideas in the theory of random media," Acta. Appl. Math, 22, 1991, Kluwer Acad. Publishers, 723 pp.
6. "A dynamo theorem," Geoph. Astrophys. Fluid Dyn., 1986, 30, 12 pp. (with A. Ruzmaikin, D. Sokolov).
7. "Intermittency of passive field in random media," Zh. Eksp. Teor., Fiz., 1985, 89, 12 pp.
8. "Kinematic dynamo in the linear velocity field," J. Fluid Mech., 1984, 144, 11 pp. (with Ja. Zeldovich, A. Ruzmaikin, D. Sokolov).
9. "Parabolic problems for the Anderson model.� Intermittency and related topics," Comm. Math. Phys., 1990, w132, 32 pp.
10. "Parabolic equations with a Levy random potential," Proc. Charlotte Conf. in Stoch. Partial Diff. Equa., Charlotte, N.C., 1992, 25 pp. (with H. Anh and R. Carmona).
11. "Intermittency and phase transition for some particle systems in random media," to appear in the Proc. Katata Symp., Japan), 1992, 20 pp. (with R. Carmona).
12. �Parabolic Anderson model and intermittency, " Preprint, UCI, 1992, 125 pp. (to appear in Memoir. Amer. Soc.) (with R. Carmona).  

VI.� Hydrodynamics and Oceanography (9)

1. "Variability of temperature field of ocean surface," DAN USSR, 1985, 283, 3 pp. (with A. Ruzmaikin, L. Piterbarg, D. Sokolov).
2. "Turbulent diffusion of impurites gradients," DAN USSR, 1985, 283, No. 5, 4 pp.
3. �Generation of the long-scale anomalies of the ocean surfaces temperature by the short period atmosphere processes," Isv. An. USSR, 1987, 5, 7 pp. (with D. Sokolov, L. Piterbarg).
4. "Localization of Rossby waves," DAN USSR, 1989, 306, 4 pp.
5. "Heat propagation in random flows," Russian J. of Math. Phys., 1992, w1, 24 pp. (with Piterbarg).

VII.� Chemistry Kinetics (12)

1. "Some properties of the percolation models of polymer aging," DAN USSR, 1988, v.
2. 302, w3, 4 pp. (with B. Gnedenko, R. Braginskii, G. Zaitzeva).
3. �Mathematical models of hierarchical polycrystal structures," DAN USSR, 1988, v. 302, w4, 4 pp. (with R. Braginskii, G. Narkunskaja, A. Reznikova).
4. �Trap correlation influence on Brownian particle death:� One dimensional case," Phys. Letters A, 1992, w161, 4 pp. (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev).
5. �Trap correlation influence on diffusion-limited process rate," Phys. Review A, 1992, v. 45, w8, (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev).
6. "Diffusion-limited reactions with correlated traps," Chem. Phys. Lett., 1992, v. 193, w4, 4 pp. (with A. Brezhkovskii, Ja. Makhnovskii, R. Suries, L. Bogachev).
7. "Brownian particle trapping on grouped traps," Phys. Review Letters, to appear, 1993, 8 pp. (with A. Berezhkovskii, Ju. Makhnovskii, L. Bogachev).

RESEARCH INTERESTS

Theory of Random Media, Spectral Theory, Intermittency and Homogenization with Applications that include oceanography and astrophysics).