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Reunion of vicious walkers: Results from epsilon -expansion

S Mukherji and S M Bhattacharjee

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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.


PACS

05.40.Fb Random walks and Levy flights

61.41.+e Polymers, elastomers, and plastics

02.50.Cw Probability theory

64.60.A- Specific approaches applied to studies of phase transitions

MSC

82B28 Renormalization group methods (See also 81T17)

82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)

81S40 Path integrals (See also 58D30)

82D60 Polymers

60G50 Sums of independent random variables; random walks

Subjects

Soft matter, liquids and polymers

Computational physics

Condensed matter: structural, mechanical & thermal

Statistical physics and nonlinear systems

Dates

Issue 22 (21 November 1993)



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