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• W1992927140 abstract "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." @default.
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• W1992927140 date "1993-05-01" @default.
• W1992927140 modified "2023-09-27" @default.
• W1992927140 title "Generalized Kontsevich model versus Toda hierarchy and discrete matrix models" @default.
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• W1992927140 doi "https://doi.org/10.1016/0550-3213(93)90347-r" @default.
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