On a few simple properties of chains with repulsive interactions

ON A FEW SIMPLE PROPERTIES OF CHAINS WITH REPULSIVE INTERACTIONS 

One-dimensional chains with repulsive interactions have properties which can be studied rigorously, and we shall describe them below. In d-dimensional space, the effect of the excluded volume on the behaviour of the chains diminishes when d increases and simple arguments show that beyond d = 4, the chains with excluded volume behave like chains with independent links (quasi-Brownian chains). 

Below four dimensions, the probability distribution of the vector joining the extremities is no longer Gaussian, and an interesting property of this distribution was established in a quasi-rigorous way by Fisher (1966).11 

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