Abstract
Friendly walkers are the non-crossing random walkers on a lattice with attractive interactions. We characterize each trajectory of friendly walkers by the number of walkers m , the time interval of observation t and the total length of trajectory r . A new algorithm to generate trajectories on a spatio-temporal plane is proposed and the distribution function of number of distinct trajectories characterized by ( m , t , r ), f m , t ( r ), is estimated by a random sampling method. The variance, the skewness and the kurtosis of f m , t ( r ) converge to finite values without scaling as t →∞ for each m . The distribution is asymmetric and its tails are expressed by stretched exponential functions. We consider the canonical distribution of m friendly walkers by introducing a parameter p which plays the same role of the Boltzmann factor e -β in the usual equilibrium systems. We calculate the mean and variance of r in the canonical distribution as a function of p for each m at t . It is observed that the varian...
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