Abstract
Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies in the 1/N expansion introduced by 't Hooft. Random tensor models generalize random matrices to theories of random higher dimensional spaces. For a long time, no viable 1/N expansion for tensors was known and their success was limited. A series of recent results has changed this situation and the extension of the 1/N expansion to tensors has been achieved. We review these results in this paper.
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