10:00 - 11:00, July 29, 2025 (Tuesday) Room 505, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館505研討室+ Cisco WebEx)
On Spectral Gap Expansion for Some Ornstein Uhlenbeck Process in Fast Incompressible Flow Brice Franke (Université de Bretagne Occidentale)
Abstract
(joint work with Shuenn-Jyi Sheu and Thi-Hien Nguyen)
In this talk, I want to present some results and open questions related to the analysis of the expansion of the spectral gap
of the family of operators
as , where is a symmetric positive definite -matrice and is an -matrice satisfying . We will see that, due to some result from Matafune, Pallara and Priola, the question can be reduced to the study of the asymptotic behavior of the eigenvalues of the matrice as . The special relationship between and enables us to obtain some iterative method for determining the coefficients of the power series expansion of the eigen values and eigen vectors of the matrix family as . This then yields information on the speed at which the gap converges as . The method works well as long as the matrice does not have eigen vectors with eigen space of dimension larger than one. Open questions remain in the general situation.
