Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Kontsevich Model Versus Toda Hierarchy and Discrete Matrix
  Models   We represent the partition function of the Generalized Kontsevich Model (GKM)
in the form of a Toda lattice $\tau$-function and discuss various implications
of non-vanishing "negative"- and "zero"-time variables: the appear to modify
the original GKM action by negative-power and logarithmic contributions
respectively. It is shown that so deformed $\tau$-function satisfies the same
string equation as the original one. In the case of quadratic potential GKM
turns out to describe {\it forced} Toda chain hierarchy and, thus, corresponds
to a {\it discrete} matrix model, with the role of the matrix size played by
the zero-time (at integer positive points). This relation allows one to discuss
the double-scaling continuum limit entirely in terms of GKM, $i.e.$ essentially
in terms of {\it finite}-fold integrals.

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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an