报告题目：On the Spectral Gap and Asymptotic Variance for Diffusion Acceleration
报告人：Dr. Sheng-Jhih Wu (吳聲志博士)
Institute of Mathematics, Academia Sinica 台湾中央研究院
时间：2014年5月8日下午16：10地点：数学楼二楼学术报告厅
报告摘要: The study of antisymmetric perturbation of reversible diffusions originates from the desire
to accelerate the convergence to the underlying probability distribution. In this talk, we will discuss
the spectral gap and asymptotic variance as the comparison criteria for the performance of diffusion
acceleration studied in our recent works. In the case of Gaussian diffusions, the dynamics of spectral
gaps lead to an interesting inverse eigenvalue problem. We explore optimal perturbations via two
aspects. One is the limiting behavior of perturbation from a family of skew-symmetric matrices as
the magnitude of the perturbation goes to infinity. The other is the attainability of the optimal rate
of convergence by direct construction of skew-symmetric matrices theoretically and numerically. In
the second part of this talk, we will discuss the asymptotic variance for diffusion acceleration. We
prove that the asymptotic variance for antisymmetrically perturbed processes is no larger than that for
the unperturbed one for both uniform analysis and worst-case analysis. In particular, we characterize
the conditions for strictly better performance. This talk is based on two joint works with Chii-Ruey
Hwang, Moody T. Chu, and Raoul Normand.