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The present work analyzes the redundancy of sets of combinatorial objectsproduced by a weighted random generation algorithm proposed by Denise et al.This scheme associates weights to the terminals symbols of a weightedcontext-free grammar, extends this weight definition multiplicatively on words,and draws words of length $n$ with probability proportional their weight. Weinvestigate the level of redundancy within a sample of $k$ word, the proportionof the total probability covered by $k$ words (coverage), the time (number ofgenerations) of the first collision, and the time of the full collection. Forthese four questions, we use an analytic urn analogy to derive asymptoticestimates and/or polynomially computable exact forms. We illustrate these toolsby an analysis of an RNA secondary structure statistical sampling algorithmintroduced by Ding et al.

Weighted random generation of context-free languages: Analysis of collisions in random urn occupancy models