论文标题
Hoffmann-Jørgensen在正面矩阵上随机步行的不平等现象
Hoffmann-Jørgensen Inequalities for Random Walks on the Cone of Positive Definite Matrices
论文作者
论文摘要
我们考虑在$ m \ times m $阳性确定矩阵上随机步行，其中底层随机矩阵在锥体上具有正交分布，而riemannian指标是圆锥上距离的度量。通过应用Khare和Rajaratnam的结果（Ann。probab。，45（2017），4101--4111），我们在锥体上随机步行而获得了Hoffmann-Jørgensen类型的不平等。对于WishArt Distribution $ W_M（A，I_M）$，带有索引参数$ A $和矩阵参数$ I_M $，IDENTITY MATRIX，我们将在Hoffmann-Jørgensen不平等中得出每个术语的显式和可计算范围。
We consider random walks on the cone of $m \times m$ positive definite matrices, where the underlying random matrices have orthogonally invariant distributions on the cone and the Riemannian metric is the measure of distance on the cone. By applying results of Khare and Rajaratnam (Ann. Probab., 45 (2017), 4101--4111), we obtain inequalities of Hoffmann-Jørgensen type for such random walks on the cone. In the case of the Wishart distribution $W_m(a,I_m)$, with index parameter $a$ and matrix parameter $I_m$, the identity matrix, we derive explicit and computable bounds for each term appearing in the Hoffmann-Jørgensen inequalities.
