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Hiring Candidate - Jing Wang

Date: December 14, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Jing Wang , University of Illinois at Urbana Champaign



Degenerate diffusions and their limiting behaviors


We discuss degenerate hypoelliptic diffusion processes and their limiting behaviors in both large time and small time. For a diffusion process on a sub-Riemannian manifold, questions related to large time behavior such as stochastic completeness and convergence to equilibrium are closely related to global geometric bounds including Ricci curvature lower bound. Small time behavior of its transition density falls into the regime of large deviation estimate, which connects to the sub-Riemannian distance.

In particular we are interested in the study of small time behavior of a general strict-degenerate diffusion process (weak Hörmander’s type), which has been a long- standing open problem. In this talk we will present a recent progress in this problem by developing a graded large deviation principle for diffusions on a nilpotent Lie group. Parts of this talk are based on joint work with Fabrice Baudoin and Gerard Ben Arous.