Search

The aim of this thesis is to generalize the results from the article [LMT] for the score of mismatched letters. This is an introductory work and it includes complete theoretical build-up of random sequence comparison, depending on parameters. At the end we prove the large deviations inequality for the proportions of mismatches. It gives probability for proportions of mismatches being near the asymptotic proportions of mismatches. This thesis also includes a fair bit of practical examples and an introduction into algorithms, used for sequence comparison.

Many recent results about the classification problem for ergodic measure preserving transformations involve global considerations about spaces of measure preserving transformations. This paper surveys recent joint work with Dan Rudolph and Benjamin Weiss in determining when various spaces of measure preserving transformations are equivalent in the sense of conjugacy preserving Borel isomorphism and in having the same generic dynamical properties.

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations., Comment: 12 pages, 7 figures, to appear Ann. Inst. H. Poincar\'e Prob. and Stat