Open strings, holography and stochastic processes

We use the correspondence between string states and local operators on the world-sheet boundary defined by vertex operators in open string theory to p ut in correspondence, holographically, the bosonic open string with the lar ge-N limit of a mechanical system living on the world-sheet boundary. We gi ve a natural interpretation of this system in terms of a one-dimensional st ochastic process and show that the correspondence takes the form of a map b etween two conformal field theories with central charge c = 24 and c = 1.