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The properties of string networks at scales well below the horizon are poorlyunderstood, but they enter critically into many observables. We argue that insome regimes, stretching will be the only relevant process governing theevolution. In this case, the string two-point function is determined up tonormalization: the fractal dimension approaches one at short distance, but therate of approach is characterized by an exponent that plays an essential rolein network properties. The smoothness at short distance implies, for example,that cosmic string lensing images are little distorted. We then add in loopproduction as a perturbation and find that it diverges at small scales. Thisneed not invalidate the stretching model, since the loop production occurs inlocalized regions, but it implies a complicated fragmentation process. Ourability to model this process is limited, but we argue that loop productionpeaks a few orders of magnitude below the horizon scale, without the inclusionof gravitational radiation. We find agreement with some features ofsimulations, and interesting discrepancies that must be resolved by futurework.Comment: 28 pages, 4 figures. v3: various small clarifications in calculations  (secs. 2 and 4) v4: ref. adde

Analytic study of small scale structure on cosmic strings