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Random Permutations with Cycle Weights V. Betz, D. Ueltschi and Y. Velenik Ann. Appl. Probab. 21, 312-331 (2011). We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a fraction of $n$, or a logarithmic power of $n$. Key words: Random permutations, cycle weights, cycle lengths, Ewens distribution. Files: PDF file, Published version, bibtex