Faces of matrix models
Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia
Partition functions of eigenvalue matrix models
possess a number of very different descriptions:
as matrix integrals, as solutions to linear
and non-linear equations,
as τ-functions of integrable hierarchies
and as special-geometry prepotentials,
as result of the action of W-operators and
of various recursions on elementary input data,
as gluing of certain elementary building blocks.
All this explains the central role of such matrix models in
modern mathematical physics:
they provide the basic "special functions"
to express the answers and relations between them,
and they serve as a dream model of what one should try
to achieve in any other field.