In the late ' 80s, Dr. Mihail was one of a handful of researchers that pioneered the theory of rapidly mixing Markov chains, fundamental stochastic processes in probability theory with applications throughout science and technology. In a pathbreaking departure from traditional "asymptotic" mathematical analysis (where does the process converge), theoretical computer science raises the question of "mixing rates" (how fast does the process converge). There are two combinatorial techniques to quantify convergence rates: "coupling" and expansion or conductance." Dr. Mihail's work first established the limitations of the former for the classical problem of approximating the permanent, and the power of the latter for the most general case of irreversible Markov chains. In the same context, she has also made contributions in a wide variety of problems that range from statistical physics (approximating the ICE model), to Edmonds matroid polytopes, quantifying Markov chain simulation techniques in software testing, and more recently generating models for Internet topologies.