REVIEW 1 cited by
Three-halves variation of geodesics in the directed landscape
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Three-halves variation of geodesics in the directed landscape
read the original abstract
We show that geodesics in the directed landscape have $3/2$-variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscape environment around an interior point has a small-scale limit. This limit is given in terms of the directed landscape with Brownian-Bessel boundary conditions. The environments around different interior points are asymptotically independent. We give tail bounds with optimal exponents for geodesic and weight function increments. As an application of our results, we show that geodesics are not H\"older-$2/3$ and that weight functions are not H\"older-$1/3$, although these objects are known to be H\"older with all lower exponents.
Forward citations
Cited by 1 Pith paper
-
Two-time spatial decorrelation for the flat KPZ fixed point
The two-time spatial covariance of the flat KPZ fixed point decays as exp(-c|x|^3), and normalized spatial averages converge to a Gaussian process with covariance equal to the space-integrated two-time correlation.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.