We review recent progress in 2D gravity coupled to d< 1 conformal matter, based on a
representation of discrete gravity in terms of random matrices. We discuss the saddle point …

In this article, we review the theory of Gaussian multiplicative chaos initially introduced by
Kahane's seminal work in 1985. Though this beautiful paper faded from memory until …

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-
dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The …

An exact conformal field theory describing a black hole in two-dimensional space-time is
found as an SL (2, openR)/U (1) gauged Wess-Zumino-Witten model. For k= 9/4, the …

In finite entropy systems, real-time partition functions do not decay to zero at late time.
Instead, assuming random matrix universality, suitable averages exhibit a growing" ramp" …

Following the discovery of spacetime anomaly cancellation in 1984 [1], string theory has
undergone rapid development in several directions. The early hope of making direct contact …

Quantum black holes are described by a large number of macroscopically indistinguishable
microstates. Correlation functions of fields outside the horizon at long time separation probe …

We review the solutions of O (N) and U (N) quantum field theories in the large N limit and as
1/N expansions, in the case of vector representations. Since invariant composite fields have …

This graduate level text describes in a unified fashion the statistical mechanics of random
walks, random surfaces and random higher dimensional manifolds with an emphasis on the …

We consider string theory in the background of the two-dimensional black hole as described
by the SL (2, R)/U (1) coset theory recently untroduced by Witten. We study the spectrum of …