Titlebook: Random Surfaces and Quantum Gravity; Orlando Alvarez,Enzo Marinari,Paul Windey Book 1991 Springer Science+Business Media New York 1991 Gra

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I. K. Kostovy of human expertise..The fundamental assumption of CBR is that .: a patient with similar symptoms will have the same diagnosis, the price of a house with similar accommodation and location will be similar, the design for a kitchen with a similar shape and size can be reused, and a journey plan is s

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On Triangles and Squares: just add any matter explicitly by giving extra (flavour) indices to the matrix that generates triangulations, then integrate out all these matrices but one. This simple argument shows that a full classification of critical behaviour in the one-matrix model may be too ambitious a task.

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Non-Perturbative Effects in 2D Gravity and Matrix Models the most interesting cases, in particular for pure gravity, the solution is defined as a solution of a non-linear differential equation of the Painlevé type and presents some non-perturbative ambiguities, related to the delicate issue of boundary conditions, which are usually attributed to some “non-perturbative effects” of the theory.

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Action Principle and Large Order Behavior of Non-Perturbative Gravitydition, we show how the formalism of ref. [4] for 2d gravity coupled to minimal (., .) conformal matter results from an action principle. Viewed as a more intrinsic formulation of 2d quantum gravity, abstracted from a matrix model underpinning, this may result in clues to a proper formulation of string field theory.

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0258-1221 on-perturbative regime before Oetober 1989 when non-perturbative equations for the string partition functions were found by using methods based on the random triangulations of surfaees. This set of methods pro­ vides a deseription of non-eritical string theory or equivalently of the coupling of matt

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Integrable Models of Two Dimensional Quantum Gravityintegrable systems of differential equations — the so called KdV hierarchy. Also, a relation to topological gravity was discovered [5]. Correlation functions for arbitrary topology were obtained, and much progress has been made in understanding non perturbative phenomena.

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