Shuffling chromosomes

The gene order of chromosomes can be rearranged by chromosomal inversions that reverse the order of segments. Motivated by a comparative study of two 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.