Reunion of vicious walkers: Results from epsilon -expansion

Abstract

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.