A common situation in modern scientific research is that the number of factors affecting quantities of interest (such as the shape of a biomolecule, changes in regional climate, or the biodiversity of the ecosystem in a certain lake) is so large that a model comprising all of them would be analytically and/or computationally intractable. A typical way of modeling such systems is to include a manageable number of explicit dynamical variables, and represent the others by some suitable statistical or stochastic terms. Much of the recent mathematical research in such stochastic systems involves the appropriate formulation of such models when the number of retained degrees of freedom is still large, and the development of analytical methods and computational approaches to characterize how the key quantities of interest are impacted by the combination of the nonlinear dynamics of the explicit variables and their stochastic driving by unresolved variables.

High-dimensional stochastic systems are being developed and explored by Rensselaer faculty in the context of microbiology, geophysics, optics, and epidemiology. Examples of recent and ongoing research includes the impact of network topology and statistics on the synchrony of a neuronal network, social influence dynamics on random networks, hydrodynamic fluctuations in suspensions of swimming microorganisms, propagation of light through a disordered active medium, the interaction of molecular motor proteins in intracellular transport, and turbulent dynamics of waves in the ocean.

Faculty Researchers:

• Chjan Lim
• John Mitchell
• Peter Kramer