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  1. Article

    Almost sure asymptotics for the continuous parabolic Anderson model

    We consider the parabolic Anderson problem ∂ t u = κΔu + ξ(x)u on ℝ+×ℝ d with initial condition u(0,x) = 1. Here κ > 0 is a diffusion constan...

    J. Gärtner, W. König, S.A. Molchanov in Probability Theory and Related Fields (2000)

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  2. Article

    Parabolic problems for the Anderson model

    This is a continuation of our previous work [6] on the investigation of intermittency for the parabolic equation (∂/∂t)u=Hu on ℝ+×ℤ d associated with the Anderson Hamiltonian H...

    J. Gärtner, S. A. Molchanov in Probability Theory and Related Fields (1998)

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    Chapter

    One Dimensional Random Walk in a Random Medium

    One of the fundamental problems in random medium (RM) theory is the relation between homogenization of the RM (i.e. the ability to describe such media at some scales as a homogeneous one) and localization. Hom...

    R. F. Anderson, S. A. Molchanov in Stochastic Models in Geosystems (1997)

  4. Article

    Stationary parabolic Anderson model and intermittency

    This paper is devoted to the analysis of the large time behavior of the solutions of the Anderson parabolic problem: $$\frac{{\partial u}}{{\p...

    R. A. Carmona, S. A. Molchanov in Probability Theory and Related Fields (1995)

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    Article

    Hyperbolic asymptotics in Burgers' turbulence and extremal processes

    Large time asymptotics of statistical solutionu(t,x) (1.2) of the Burgers' equation (1.1) is considered, whereξ(x)=ξ L(x) is a stationary zero mean Gaussian process depending on a large parameterL>0 so that ...

    S. A. Molchanov, D. Surgailis, W. A. Woyczynski in Communications in Mathematical Physics (1995)

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    Article

    Infinite-scale percolation in a new type of branching diffusion process

    We give an account and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They lead to a novel type of stochastic process, namely branching pro...

    A. Mezhlumian, S. A. Molchanov in Journal of Statistical Physics (1993)

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    Article

    Limiting eigenvalue distribution for band random matrices

    S. A. Molchanov, L. A. Pastur, A. M. Khorunzhii in Theoretical and Mathematical Physics (1992)

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    Article

    Mean-field models in the theory of random media. III

    L. V. Bogachev, S. A. Molchanov in Theoretical and Mathematical Physics (1991)

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    Article

    Structure of spectrum edge for multidimensional Anderson model

    L. N. Grenkova, S. A. Molchanov, Yu. N. Sudarev in Theoretical and Mathematical Physics (1990)

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    Article

    Parabolic problems for the Anderson model

    The objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics, in particular in hydrodynamics. On a qualitative...

    J. Gärtner, S. A. Molchanov in Communications in Mathematical Physics (1990)

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    Article

    Mean-field models in the theory of random media. II

    L. V. Bogachev, S. A. Molchanov in Theoretical and Mathematical Physics (1990)

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    Article

    Mean-field models in the theory of random media. I

    L. V. Bogachev, S. A. Molchanov in Theoretical and Mathematical Physics (1989)

  13. No Access

    Article

    Wave transmission coefficients for one-dimensional random barriers

    A. V. Marchenko, S. A. Molchanov, L. A. Pastur in Theoretical and Mathematical Physics (1989)

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    Article

    Percolation in random fields. III

    S. A. Molchanov, A. K. Stepanov in Theoretical and Mathematical Physics (1986)

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    Article

    Percolation in random fields. II

    S. A. Molchanov, A. K. Stepanov in Theoretical and Mathematical Physics (1983)

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    Article

    Percolation in random fields. I

    S. A. Molchanov, A. K. Stepanov in Theoretical and Mathematical Physics (1983)

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    Article

    On a one-dimensional spin system

    S. A. Molchanov, Nguyen The Long in Theoretical and Mathematical Physics (1975)