Reunion of vicious walkers: Results from epsilon -expansion
- 21 November 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (22) , L1139-L1144
- https://doi.org/10.1088/0305-4470/26/22/002
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.Keywords
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