Universal shape ratios for open and closed random walks: exact results for all d

Abstract

The mean asphericities (Ad) of open and closed Gaussian polymer chains are computed exactly and analytically (up to simple quadratures) for arbitrary space dimensions d. Excellent agreement is found with existing simulation data for d=2, 3, and 4. The authors' technique can also be used to compute other averages of ratios of fluctuating variables as well as extended to include the effects of self-avoiding walk interactions.