6 problems

Last passage percolation assigns random weights to vertices and studies the maximum accumulated weight over directed paths. In the first model considered here, the weights are inde…

A Lévy matrix $\mathbf{H}$ is a symmetric random matrix whose entries are random variables in the domain of attraction of an $\alpha$-stable law; let $\mu_\mathbf{H}$ denote its em…

Mixed-mechanism large-deviations conjecture. No finite number of large jobs suffices; instead, the large deviations behavior should be driven by a combination of light- and heavy-t…

Utility-functional tail conjecture. Assume that $\bar F\in\mathcal{S}$ and $f(x)=x^k$. Then

Workload-area conjecture. If $\bar F\in\mathcal{S}$, then

Queue-area tail conjecture. If $F\in\mathcal{S}$, then