论文标题
与高斯beta集合相关的对称三角形基质值的特征值过程
Eigenvalue processes of symmetric tridiagonal matrix-valued processes associated with Gaussian beta ensemble
论文作者
论文摘要
我们通过将独立的Brownian Motions和Bessel过程分别放在对角线条目和diagonal的对称性beta集合和贝塞尔过程中，考虑与高斯β集合（g $β$ e）相关的对称三角基矩阵值。然后，我们得出了特征值过程所满足的随机微分方程，并表明其（索引）主次要子矩阵的特征值出现在随机微分方程中。通过凯奇（Cauchy）对特征值的交错论点，我们可以表征特征值过程几乎肯定地通过贝塞尔（Bessel）过程的维度肯定地相互碰撞的充分条件。
We consider the symmetric tridiagonal matrix-valued process associated with Gaussian beta ensemble (G$β$E) by putting independent Brownian motions and Bessel processes on the diagonal entries and upper (lower)-diagonal ones, respectively. Then, we derive the stochastic differential equations that the eigenvalue processes satisfy, and we show that eigenvalues of their (indexed) principal minor sub-matrices appear in the stochastic differential equations. By the Cauchy's interlacing argument for eigenvalues, we can characterize the sufficient condition that the eigenvalue processes never collide with each other almost surely, by the dimensions of the Bessel processes.
