String interactions in c=1 matrix model

We study string interactions in the fermionic formulation of the c=1 matrix model. We give a precise nonperturbative description of the rolling tachyon state in the matrix model, and discuss S-matrix elements of the c=1 string. As a first step to study string interactions, we compute the interaction of two decaying D0-branes in terms of free fermions. This computation is compared with the string theory cylinder diagram using the rolling tachyon ZZ boundary states. (author)