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.

No of pages: 11, 1figure on request, Revtex3,IP/BBSR/9297

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