Random Media

1. Front Matter

   Pages i-xi

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2. Stable Convergence and Asymptotic Capacity Measures

   • J. R. Baxter, N. C. Jain

   Pages 1-13

3. Effective Equation and Renormalization for a Nonlinear Wave Problem with a Random Source

   • Luis L. Bonilla

   Pages 15-27

4. The Spectrum of Backscatter for Pulse Reflection from a Randomly Stratified Medium

   • R. Burridge, G. Papanicolaou, B. White

   Pages 29-43

5. Exercises for a Book on Random Potentials

   • René Carmona

   Pages 45-65

6. Travel-Time Problems for Waves in Random Media

   • P. L. Chow

   Pages 67-88

7. Elements of the Theory of Amorphous Semiconductors

   • Morrel H. Cohen

   Pages 89-108

8. Multidimensional RWRE with Subclassical Limiting Behavior

   • Richard Durrett

   Pages 109-119

9. Localization for a Random Discrete Wave Equation

   • William G. Faris

   Pages 121-128

10. Simulations and Global Optimization

    • Basilis Gidas

    Pages 129-145

11. Low Temperature Behavior in Random Ising Models

    • John Z. Imbrie

    Pages 147-162

12. Some Recent Results on Wave Equations, Path Integrals, and Semiclassical Approximations

    • John R. Klauder

    Pages 163-182

13. Effective Conductivities of Reciprocal Media

    • Joseph B. Keller

    Pages 183-188

14. Reflection from a Lossy, One-Dimensional Ocean Sediment Model

    • Werner E. Kohler

    Pages 189-209

15. Problems of One-Dimensional Random Schrödinger Operators

    • Shinichi Kotani

    Pages 211-214

16. Numerical Simulation of Itô Stochastic Differential Equations on Supercomputers

    • W. P. Petersen

    Pages 215-228

17. Lyapunov Exponent and Rotation Number of the Stochastic Harmonic Oscillator

    • Mark A. Pinsky

    Pages 229-243

18. Regularity of the Density of States for Stochastic Jacobi Matrices: A Review

    • Barry Simon

    Pages 245-266

19. Limit Theorems for Measure-Valued Diffusion Processes that Arise in Wave Propagation in a Randomly Inhomogenous Ocean

    • Halil Mete Soner

    Pages 267-278

20. Spectral Properties of Discrete and Continuous Random Schrödinger Operators: A Review

    • Bernard Souillard

    Pages 279-291

This IMA Volume in Mathematics and its Applications RANDOM MEDIA represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: Daniel Stroock (Chairman) \~ende 11 Fl emi ng Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especi ally thank George Papani col aOIJ for organi zi ng a workshop which produced fruitful interactions between mathematicians and scientists from both academia and industry. George R. Sell Hans I~ei nherger PREFACE During September 1985 a workshop on random media was held at the Institute for Mathematics and its Applications at the University of Minnesota. This was part of the program for the year on Probability and Stochastic Processes at IMA. The main objective of the workshop was to bring together researchers who work in a broad area including applications and mathematical methodology. The papers in this volume give an idea of what went on and they also represent a cross section of problems and methods that are currently of interest.

• Parameter
• differential equation
• diffusion process
• stochastic differential equation
• stochastic equation

• Institute for Mathematics and Its Applications, Minneapolis, USA

  George Papanicolaou

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