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The title High Dimensional Probability is used to describe the
many tributaries of research on Gaussian processes and probability
in Banach spaces that started in the early 1970s. Many of the
problems that motivated researchers at that time were solved. But
the powerful new tools created for their solution turned out to be
applicable to other important areas of probability. They led to
significant advances in the study of empirical processes and other
topics in theoretical statistics and to a new approach to the study
of aspects of Levy processes and Markov processes in general. The
papers in this book reflect these broad categories. The volume thus
will be a valuable resource for postgraduates and reseachers in
probability theory and mathematical statistics."
The title High Dimensional Probability is an attempt to describe
the many trib utaries of research on Gaussian processes and
probability in Banach spaces that started in the early 1970's. In
each of these fields it is necessary to consider large classes of
stochastic processes under minimal conditions. There are rewards in
re search of this sort. One can often gain deep insights, even
about familiar processes, by stripping away details that in
hindsight turn out to be extraneous. Many of the problems that
motivated researchers in the 1970's were solved. But the powerful
new tools created for their solution, such as randomization,
isoperimetry, concentration of measure, moment and exponential
inequalities, chaining, series representations and decoupling
turned out to be applicable to other important areas of
probability. They led to significant advances in the study of
empirical processes and other topics in theoretical statistics and
to a new ap proach to the study of aspects of Levy processes and
Markov processes in general. Papers on these topics as well as on
the continuing study of Gaussian processes and probability in
Banach are included in this volume."
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