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.

Stable Convergence and Asymptotic Capacity Measures.- Effective Equation and Renormalization for a Nonlinear Wave Problem with a Random Source.- The Spectrum of Backscatter for Pulse Reflection from a Randomly Stratified Medium.- Exercises for a Book on Random Potentials.- Travel-Time Problems for Waves in Random Media.- Elements of the Theory of Amorphous Semiconductors.- Multidimensional RWRE with Subclassical Limiting Behavior.- Localization for a Random Discrete Wave Equation.- Simulations and Global Optimization.- Low Temperature Behavior in Random Ising Models.- Some Recent Results on Wave Equations, Path Integrals, and Semiclassical Approximations.- Effective Conductivities of Reciprocal Media.- Reflection from a Lossy, One-Dimensional Ocean Sediment Model.- Problems of One-Dimensional Random Schrödinger Operators.- Numerical Simulation of I to Stochastic Differential Equations on Supercomputers.- Lyapunov Exponent and Rotation Number of the Stochastic Harmonic Oscillator.- Regularity of the Density of States for Stochastic Jacobi Matrices: a Review.- Limit Theorems for Measure-Valued Diffusion Processes that Arise in Wave Propagation in a Randomly Inhomogenous Ocean.- Spectral Properties of Discrete and Continuous Random Schrodinger Operators: a Review.- Dispersive Bulk Parameters for Coherent Propagation in Correlated Random Distributions.- Random Rays and Stochastic Caustics.