Matrix Models of Two-Dimensional Gravity and Discrete Toda Theory
نویسنده
چکیده
Recursion relations for orthogonal polynominals, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equvalent to the equations of the Todachain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.
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