Let Pi be the directed geodesic from (0,0) to (0,1) in the directed landscape. For each t∈[0,1/2), define the increment process eta_t colon[0,1/2]→R by eta_t(s)=Pi(t+s)-Pi(t). Then, for every 0≤ t 0.

Dauvergne–Ortmann–Virág Conjecture 14.5

Dauvergne, Ortmann, and Virág posed the conjecture in their 2022 paper on the directed landscape. It asks for an if-and-only-if absolute-continuity criterion for directed-landscape increment processes and identifies an exceptional initial point.

Known results

Sarkar and Virág proved an earlier one-sided absolute-continuity result.
Tassopoulos and Sarkar reported mutual absolute continuity with Brownian motion of diffusion parameter $2$ for KPZ fixed-point increments, for $t>0$ and arbitrary admissible initial data.

September 30, 2026 claimed resolution

Tassopoulos and Sarkar claim that their theorem establishes the full stated criterion and settles Conjecture $14.5$ . The claim is supported by an unrefereed preprint and has no independent expert assessment or verification.

Current status (as of October 2026): The criterion is claimed in a recent preprint, but the conjecture remains unverified.

Dauvergne–Ortmann–Virág Conjecture 14.5

Primary source

Additional references

Progress summary

Solutions 0