The PI proposes to conduct research on quasirandom analogues of discrete random systems, both as tools for simulation problems and as objects of study in their own right. Quasirandom simulation schemes often are just as fast as random simulations schemes, and when applied to estimation problems typically give smaller error. The PI's research will study such schemes, and will explore new ways of removing the ``noise'' from random systems while retaining key features of their average-case behavior, building on earlier work by the PI, Lionel Levine, Yuval Peres, Josh Cooper, and Joel Spencer, among others. The resulting non-random systems exhibit startling symmetry and unexpected structure that call out for explanation.
Current technology depends heavily on simulation, and many existing methods of simulation make use of randomness, whether or not the system being simulated has a random element to it. This ``Monte Carlo Method'' has had huge success in the past century. My work will explore the notion that in many cases, what makes Monte Carlo work is not randomness per se but certain regularities that are consequences of randomness. By bringing these regularities to the fore and jettisoning randomness itself, one should be able to devise general methods of simulation that are more accurate.
