Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random matrices, Virasoro algebras, and noncommutative KP   What is the connection of random matrices with integrable systems? Is this
connection really useful? The answer to these questions leads to a new and
unifying approach to the theory of random matrices. Introducing an appropriate
time t-dependence in the probability distribution of the matrix ensemble, leads
to vertex operator expressions for the n-point correlation functions
(probabilities of n eigenvalues in infinitesimal intervals) and the
corresponding Fredholm determinants (probabilities of no eigenvalue in a Borel
subset E); the latter probability is a ratio of tau-functions for the
KP-equation, whose numerator satisfy partial differential equations, which
decouple into the sum of two parts: a Virasoro-like part depending on time only
and a Vect(S^1)-part depending on the boundary points A_i of E. Upon setting
t=0, and using the KP-hierarchy to eliminate t-derivatives, these PDE's lead to
a hierarchy of non-linear PDE's, purely in terms of the A_i. These PDE's are
nothing else but the KP hierarchy for which the t-partials, viewed as commuting
operators, are replaced by non-commuting operators in the endpoints A_i of the
E under consideration. When the boundary of E consists of one point and for the
known kernels, one recovers the Painleve equations, found in prior work on the
subject.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: adap-org