Daniel Spivak | Searcharxiv

arXiv2025

One-point large deviations of the directed landscape geodesic

The directed landscape, the central object in the Kardar-Parisi-Zhang universality class, is shown to be the scaling limit of various models by Dauvergne and Vir\'ag (2022) and Dauvergne, Ortmann and Vir\'ag (2018). In his study of geodesics in upper tail deviations of the directed landscape, Liu (2022) put forward a conjecture about the rate of the lowest rate metric under which a geodesic between two points passes through a particular point between them. Das, Dauvergne and Vir\'ag (2024) disproved his conjecture, and made a conjecture of their own. This paper disproves that conjecture and puts the question to rest with an answer and a proof.

math.PR↗

arXiv2017

An infinite quantum Ramsey theorem

We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided there is no obvious obstruction, there is an infinite rank projection P with the property that the compression PVP is either maximal or minimal in a certain natural sense.

math.OA↗