6 problems

Let $G$ be a weight distribution on the non-negative reals, and assign independent passage times with distribution $G$ to the edges of the square lattice $\mathbb{Z}^2$. For a fini…

Let $X$ be a fractional-Green Gaussian process on $[0,1]$, meaning that its covariance eigenvalue problem reduces to a generalized eigenproblem … with the boundary conditions defin…

For $m\in\mathbb{N}$, let $W_m^{[\beta_1,\ldots,\beta_m]}$ be the $m$-times integrated Wiener process, where each $\beta_j$ is either $0$ or $1$. In the small-ball asymptotic … whe…

Let $(\mu_k)$ and $(\tilde{\mu}_k)$ be the positive eigenvalues of two covariance operators, and suppose the corresponding Gaussian norms have small-ball probabilities whose compar…

Let $\mu$ be a product measure satisfying the assumptions that the full product measure exists and that the scaled marginals satisfy the stated conditions. Let $E_{\gamma,m}$ be th…

For $c>1/2$, consider the $m$-times integrated processes $(S^{(c)})_m^{[\beta_1,\ldots,\beta_m]}$. The processes $(S^{(c)})_m^{[0,\ldots,0]}$ and $(S^{(c)})_m^{[1,\ldots,1]}$ have…