Large order behavior of non-perturbative gravity

We study the large order behavior and Borel summability of the topological expansion of models of 2D gravity coupled to matter. We treat in particular the cases of pure gravity, and gravity coupled to Yang-Lee, Ising, and tricritical Ising matter. We then discuss arbitrary one-matrix models and gravity coupled to general (p, q) conformal matter, in particular showing that the genus-k contribution to their partition functions goes asymptotically for large k as Γ(2k-1/2). Finally, we show that the large order behavior analysis for the one-matrix models coincides with an instanton calculation of barrier penetration effects. (orig.)