Whole-Exome Sequencing Study of Thyrotropin-Secreting Pituitary Adenomas

学位記番号：医博甲169

Random matrix ensembles: Wang-Landau algorithm for spectral densities

We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to simultaneously investigate the thermodynamic properties. This approach is a powerful alternative to the conventionally used Monte Carlo simulations based on the Boltzmann sampling, and is ideally suited for investigating beta-ensembles.Comment: 8 pages, 5 figures, To appear in EP

On classification of typical representations for GL3(F){\rm GL}_3(F)

Let $F$ be any non-Archimedean local field with residue field of cardinality $q_F$. In this article, we obtain a classification of typical representations for the Bernstein components associated to the inertial classes of the form $[{\rm GL}_n(F)\times F^\times, \sigma\otimes\chi]$ with $q_F>2$, and for the principal series components with $q_F>3$. With this we complete the classification of typical representations for ${\rm GL}_3(F)$, for $q_F>2$.Comment: Final accepted versio