Nonperturbative effect in c=1 noncritical string theory and Penner model

We derive the effect of instantons in the Penner model. It is known that the free energies of the Penner model and the c=1 noncritical string at self-dual radius agree in a suitable double scaling limit. On the other hand, the instanton in the matrix model describes a nonperturbative effect in the noncritical string theory. We study the correspondence between the instantons in the Penner model and the nonperturbative effect in c=1 noncritical string at self-dual radius.