Eigenvalues of the covariance matrix of the Wiener process

Question

Let $t_1< \dots < t_p$ be distinct points within $(0,1)$ and consider the $p \times p$ matrix $\mathbf{C}$ with entries $$c_{ij} = \min(t_i,t_j)$$ Please note that this is a well-known matrix as it is the covariance matrix of the Wiener process on $(0,1)$. I have been wondering if there exist closed form expressions for its eigenvalues. I am particularly interested in the behavior of the largest and smallest eigenvalues of this matrix as a function of $p$. References are also welcome, as this question is likely to have been asked and answered before. Thank you.