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This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on'Emerging Applications of Probability.'We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit­ ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of­ fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica­ tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz­ ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo­ spheric physics, fluid mechanics, seismology, and oceanography. The com­ mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.