Abstract
After a general review of the matrix model approach to the discretized two-dimensional quantum gravity a model of discretized bosonic strings in the 1D target space is considered in detail. A recently found non perturbative solution is discussed and investigated. Some aspects of this model, such as nonperturbative stability and renormalized physical obervables, are clarified. A compactified (finite temperature) version of this model is shown to be reducible to an integrable N-body problem of Calogero type.
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