報告題目：Smallest Eigenvalue of Large Hankel Matrices at critical point
騰訊會議(ID)：685 785 547
報告摘要：We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. We study a family of Hankel matrices generated by the weight w(x)=exp(x^β), supported on [0, ∞) and β>0. In the situation where β>1/2, the smallest eigenvalue tend to 0, exponentially fast as N gets large. If β<1/2, the situation where the classical moment problem is indeterminate, the smallest eigenvalue is bounded from below by a positive number for all N, including infinity. If β=1/2, it is conjectured that the smallest eigenvalue tends to 0 algebraically, with a precise exponent.
報告人簡介： Chen Yang, received his Phd in the University of Massachusetts, did his Post-Doc at the Cavendish Laboratory, Cambridge University,?University of Karlsruhe,?and the Max Planck Institute, Stuggart, before he joined Imperial College London, in 1992. Chen become Professor of Mathematical Physics in 2004,? then he moved to the University of Macau in 2012?as Professor of Mathematics. He works in Random Matrix Theory and problems related to integrable systems.