Mechanism for superuniversal behavior in certain stochastic systems

The problems of a directed polymer in a random matrix, a randomly stirred fluid obeying Burger's equation, and the dynamics of an interface growing by vapor deposition can be mapped into each other. Renormalization-group arguments suggest that there is an upper critical dimension for these systems above which the correlation length exponent {ν} should be (1/2. We present an argument which suggests that {ν}=(2/3 in all dimensions (that is, it is superuniversal), in agreement with the conjecture and numerical simulations of Kardar and Zhang.