Our basic question is: Given a collection of DNA sequences, what underlying forces are
responsible for the observed patterns of variability? To approach this question we introduce …

Abstract Let Y=(y 1, y 2,...), y 1≥ y 2≥..., be the list of sizes of the cycles in the composition
of cn transpositions on the set {1, 2,..., n}. We prove that if c> 1/2 is constant and n→∞, the …

In this paper, a random graph process {G (t)} t≥ 1 is studied and its degree sequence is
analyzed. Let {W t} t≥ 1 be an iid sequence. The graph process is defined so that, at each …

Abstract Models of evolution by genome rearrangements are prone to two types of flaws:
One is to ignore the diversity of susceptibility to breakage across genomic regions, and the …

Molecular evolutionary methods and tools are difficult to validate as we have almost no
direct access to ancient molecules. Inference methods may be tested with simulated data …

A bstract The basic idea of quantum complexity geometry is to endow the space of unitary
matrices with a metric, engineered to make complex operators far from the identity, and …

Let S_n be the permutation group on n elements, and consider a random walk on S_n
whose step distribution is uniform on k-cycles. We prove a well-known conjecture that the …

Consider the random walk on the permutation group obtained when the step distribution is
uniform on a given conjugacy class. It is shown that there is a critical time at which two …

We examine the number of cycles of length k in a permutation as a function on the symmetric
group. We write it explicitly as a combination of characters of irreducible representations …

We determine the log-Sobolev constant of the multi-urn Bernoulli–Laplace diffusion model
with arbitrary parameters, up to a small universal multiplicative constant. Our result extends …