Abstract.The gene order of chromosomes can be rearranged by chromosomal inversions that reverse the order of segments. Motivated by a comparative study of two {\it Drosophila} species, we investigate the number of reversals that are needed to scramble the gene order when all reversals are equally likely and when the segments reversed are never more than $L$ genes. In studying this question we prove some new results about the convergence to equilibrium of shuffling by transposition and the one dimensional simple exclusion process.
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