about their own work. Since much of this work has been or is being published
elsewhere, it seemed most useful not to include in the volume any of the complete
texts of the talks, but instead to include two- or three-page-long extended abstracts
of all of them. With the cooperation of almost all of the speakers this is what has
been done. The abstracts show that the subject is by no means isolated, that there
is already a healthy amount of work done on probabilistic aspects and on buildings,
and that applications reach as far as financial mathematics. The abstracts are long
enough to state clearly their authors' results, and together they give a good picture
of what the present concerns of researchers in the subject are.
Maybe a few words should also be said about what the volume does not contain:
finite graphs are almost completely absent, despite their importance. They are the
natural analogues of compact Riemannian manifolds, and harmonic functions and
forms together with random walks on them are active subjects of research both
in their own right and for applications to electric networks and communications
networks, among other things.
The finite and infinite theories at present have somewhat different flavors, and
there has not been very much contact between workers in the two directions. It
is more than likely that more contact would be of benefit to all. However, the
limitations on the size of our workshop made it impractical to try to expand it in
this direction.
It remains for the editor-organizer to express his thanks to all who made the
workshop and this volume possible; first of all to the authors of the minicourses
for their hard work in preparing, delivering, and writing down their lectures in a
finished form;
to the speakers for their participation and for accepting the extra
work of writing up extended abstracts of their talks; to all other participants of the
workshop; to the Graduate Center of CUNY for use of its facilities; and last but
not least to the National Science Foundation of the USA, without whose grant the
workshop could not have taken place.
Adam Koninyi
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