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-J{\o}rgensen 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-J{\o}rgensen inequalities.

翻译：我们认为,在以百万美元计时的圆锥体上随机行走是肯定的矩阵,其中基本随机矩阵在锥体和里曼尼度量值上具有或正反差分布,这是测量锥体距离的尺度。通过应用哈雷和拉贾拉特南(Ann. Probab., 45 (2017), 4101-4111)的结果,我们获得在锥体上随机行走的霍夫曼-J(o}rgensen)类型的不平等。在Wishart 分布 $_m(a, I_m) 的情况下,Wishart 分配 $W_m(a, I_m) $(a) 指数参数和矩阵参数 $I_m(m) 身份矩阵中,我们得出了霍夫曼-J(o) rgensen 不平等中出现的每个术语的明确和可计算界限。