For arbitrary random walks in any d-dimensional space, a 1/d expansion of the most probable size ratio, i.e., squared radius of gyration s2 divided by 〈s2〉 of open random walks, has been developed, which, at O(1/d3), yields a very good approximation to the exact value for chains (d ⩾ 2)...

For arbitrary random walks in any d-dimensional space, expansions in powers of 1/d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/d3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells...