S Mukherji and S M Bhattacharjee 1993 J. Phys. A: Math. Gen. 26 L1139 doi:10.1088/0305-4470/26/22/002
S Mukherji and S M Bhattacharjee
Show affiliationsThe 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.
05.40.Fb Random walks and Levy flights
61.41.+e Polymers, elastomers, and plastics
64.60.A- Specific approaches applied to studies of phase transitions
82B28 Renormalization group methods (See also 81T17)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Soft matter, liquids and polymers
Issue 22 (21 November 1993)
S Mukherji and S M Bhattacharjee 1993 J. Phys. A: Math. Gen. 26 L1139
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