6 problems

Let $H^{\alpha}({\mathbf x},{\mathbf y})$ be the Busemann function in direction $e^{i\alpha}$, defined from the passage-time difference between the vertices associated with…

Non-expansiveness conjecture. The resolvent in should be non-expansive.

Busani's universality conjecture. The SH is the universal scaling limit of Busemann processes of last-passage percolation models in the KPZ class.

For $T>0$, let $d4cd^T=d4cd^T(y)$ denote the KPZ line ensemble and let $d4d5^T(x,y)$ denote the KPZ sheet. For points on the line ensemble, write $d4cd^T[(x,k)\to(y,1)]$ for the po…

Let $M$ be a symmetric space of noncompact type. A function $f:M\to\mathbb{R}$ is convex if it is convex in the sense used for functions on $M$, and a Busemann function is a functi…

Let $\Xi$ denote the exceptional set of directions appearing in the classification of semi-infinite geodesics in the directed landscape. A Busemann geodesic is a semi-infinite geod…