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Research

Probability

Probability is the study of uncertainty or randomness and its consequences in the world around us. Probability plays a significant role in almost every branch of science, engineering, economics and medicine. It is also provides the basis for statistics. Moreover, the increasing complexity of deterministic processes has stimulated investigators both in and outside of mathematics to consider probabilistic approaches. "Probability provides a way of thinking about the world that is distinct from the modes of thought in other areas of mathematics. ...Based on its special intuition, probability generates tools and techniques that are relevant to other areas of pure mathematics." --2002 NSF report on Current and Emerging Research Opportunities in Probability.

Current broad areas of probabilistic research at Tufts include stochastic processes, stochastic analysis, stochastic differential equations, attractors in non-extensive statistical mechanics, non-commutative probability, quantum information theory, plus connections with dynamical systems, mathematical physics, and functional analysis.

A recent major project of this group focused on continuous time random walks, stochastic differential equations and fractional order Kolmogorov equations. This triad of topics and their inter-relationships model complex processes arising in such areas as non-extensive statistical mechanics, financial mathematics, geology, hydrology and cell biology.

Faculty: Hahn, Hasselblatt
Current postdoc: Garmirian