Dan Stein (New York University; SFI Science Board Co-Chair)
Abstract. Complex systems are generally characterized by a high degree of metastability. In such cases it is often useful to characterize their dynamical behavior as a random walk on a "rugged landscape". There are many approaches toward studying this generic problem, and it remains a common theme in the mathematical analysis of the evolution of complex systems. While there are many analytical and numerical results, rigorous results are less common. In this talk, I will demonstrate that the random walk in an appropriate limit maps to the seemingly unrelated problem of invasion percolation, and that this in turn leads to some novel, and often surprising and unexpected, dimension-dependent behavior. If time permits, some possible applications will be discussed.