The probability research group is primarily focused on discrete probability topics. Random graphs and percolation models (infinite random graphs) are studied using stochastic ordering, subadditivity, and the probabilistic method, and have applications to phase transitions and critical phenomena in physics, flow of fluids in porous media, and spread of epidemics or knowledge in populations. Convergence rates to equilibrium in Markov chains are studied and applied to Markov Chain Monte Carlo simulation, and related algorithms for perfect sampling are created and analyzed. Various probabilistic and other techniques are used to analyze the performance of algorithms in computer science used for such purposes as sorting and searching. A plethora of interesting questions and applications allow us to involve both undergraduate and graduate students in valuable research in modern probability and stochastic processes.
For more details about the faculty, research topics, and course offerings in probability and stochastic processes, please explore the additional tabs.