The topological matrix model of the c = 1 string

We derive a Kontsevich-type matrix model for the c = 1 string directly from the W_∞ solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the Penner and Kontsevich cases, and we study its quantum effective action. The simplicity of our model leads to an encouraging interpretation in the context of background-independent non-critical string field theory.