The Shapes of Random Walks with Fixed End-to-End Distance
Fixed length random walks embedded in d spatial dimensions are discussed. As a representation of polymers, they correspond to long chain molecules whose heads and tails are fixed in space. An exact analytical expression for the asphericity is presented that is valid in arbitrary spatial dimensionality. We also present expressions for the average principal radii of gyration to order 0(1/d). These expressions recover the results for both unrestricted open and closed random walks.
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