Jing Wang (Purdue)
We study the subLaplacian L on a contact Riemannian manifold M. L is a symmetric diffusion operator which is subelliptic but nowhere elliptic. We obtain the BakryÉmery type criterion (curvaturedimension inequality) for L which gives an analytic approach to the geometric property. As a consequence, we prove that under suitable geometric bounds, spectral gap estimates can be obtained as well as the convergence to the equilibrium of the associated Markov processes. This is a joint work with F. Baudoin. top of page

Nevena Maric (Missouri)
Random walk on naturals with negative drift and absorption at 0, when conditioned on survival, has uncountably many invariant measures (quasistationary distributions, qsd). We study a FlemingViot (FV) particle system driven by this process. In this particle system there are N particles where each particle evolves as the random walk described above. As soon as one particle is absorbed, it reappears, choosing a new position according to the empirical measure at that time. Between the absorptions, the particles move independently of each other. Our focus is in the relation of empirical measure of the FV process with qsds of the random walk.
Firstly, mean normalized densities of the FV unique stationary measure converge to the minimal qsd, as N goes to infinity. Moreover, every other qsd of the random walk corresponds to a metastable state of the FV particle system. top of page
