On gyration radius distributions of star-like macromolecules

Using the path integral approach, we obtain characteristic functions of gyration radius distributions for Gaussian star and rosette macromolecules. We derive analytical expressions cumulants both distributions. Applying steepest descent method, estimate probability distribution in limit a large number arms two limiting regimes: strongly expanded collapsed show that cases, regime relative to its mean-square value, can be described by functions. In shrunk macromolecule regime, tend zero faster than any power radius. Based on asymptotic behavior statistical dispersions, demonstrate function is more densely localized near maximum polymer. construct interpolation formula which help take into account conformational entropy flexible macromolecules within Flory-type mean-field theories