Reunion of vicious walkers: Results from epsilon -expansion

The anomalous exponent, eta p , for the decay of the reunion probability of p vicious walkers, each of length N, in d (=2- epsilon ) dimensions, is shown to come from the multiplicative renormalization constant of a p directed polymer partition function. Using renormalization group (RG) we evaluate eta p to O( epsilon 2 ). The survival probability exponent is eta p /2. For p=2, our RG is exact and eta p stops at O( epsilon ). For d=2, the log corrections are also determined. The number of walkers that are sure to reunite is 2 and has no epsilon expansion.