Research Areas Probability Stochastic processes Random structures and algorithms

James Allen Fill, an emeritus professor of applied mathematics and statistics, focuses on probability and stochastic processes, with work lying at the interface with theoretical computer science. He holds a secondary appointment in the Department of Computer Science.

Fill’s research on Markov chains has focused on rates of convergence to stationarity, hitting times, and perfect simulation. He co-authored work introducing and developing strong stationary duality (SSD), a powerful technique for bounding mixing times for Markov chains, and he has written several papers applying SSD and other techniques to probabilistic analysis of self-organizing data structures for dynamic file maintenance. In addition, he created two general algorithms, “Fill’s algorithm” and “Randomness Recycler,” that modify existing Markov chain Monte Carlo algorithms to produce samples perfectly from a desired (stationary) distribution.

Fill is a leader in the analysis of algorithms (AofA) community. He is known for a series of papers with Svante Janson of Uppsala University giving an in-depth analysis of the QuickSort sorting algorithm, the AofA revolution he has led by providing more realistic analyses of key-comparison algorithms such as QuickSort and QuickSelect in terms of symbol-comparison counts, and his fundamental work with the late Philippe Flajolet and Nevin Kapur on the singularity analysis of Hadamard products of generating functions. All told, he has written more than 25 AofA-related papers.

Fill has made research contributions to a variety of additional topics, including large deviation probabilities, small deviations, percolation, and first-passage percolation, random graphs, minimal spanning trees, Radon transforms, projection pursuit, matrix analysis, partially ordered sets, applied game theory, partitions, and mathematical problems in music.

Current interests include the geometry and simulation of multivariate (Pareto) records.

Fill is a Fellow of the American Mathematical Society and of the Institute of Mathematical Statistics, and a member of the American Statistical Association, the Association for Computing Machinery, and the Mathematical Association of America. He also is the long-standing editor-in-chief of the Journal of Theoretical Probability and has been an associate editor for the Annals of Applied Probability, the Electronic Journal of Probability, and Electronic Communications in Probability. A guest editor and referee for numerous other publications, Fill is a four-time recipient of the Professor Joel Dean Award for Excellence in Teaching for the Department of Applied Mathematics and Statistics at Johns Hopkins.

Fill received his bachelor’s degree with a double major in mathematics and statistics from the University of Illinois in 1976. He then earned a master’s degree and PhD in statistics from the University of Chicago in 1979 and 1980, respectively. Fill worked as an assistant professor of statistics at Stanford University before joining the Whiting School of Engineering faculty in 1988 and has held visiting positions at the University of Chicago, MIT, and Microsoft Research.