6 papers · 1 filter
Geometry of semi-infinite geodesics in the Airy line ensemble
Pantelis Tassopoulos, Sourav Sarkar
We study the geometry of semi-infinite geodesics in the Airy line ensemble. We establish sharp estimates for disjointness probabilities involving geodesics with nearby directions a…
The starting point of a directed geodesic is special
Pantelis Tassopoulos, Sourav Sarkar
For any , consider the process defined by , where is the directed geodesic from to in the direc…
The KPZ fixed point and Brownian motion share the same null sets
Pantelis Tassopoulos, Sourav Sarkar
We show that the increments of the KPZ fixed point started from arbitrary initial data are \emph{mutually} absolutely continuous with respect to Brownian motion with diffusion para…
Quantitative Brownian regularity of the KPZ fixed point with arbitrary initial data
Pantelis Tassopoulos, Sourav Sarkar
We show that the spatial increments of the KPZ fixed point starting from arbitrary initial data, exhibit strong quantitative comparison against rate two Brownian motion on compacts…
Radon-Nikodym derivative of inhomogeneous Brownian last passage percolation
Pantelis Tassopoulos, Sourav Sarkar
We show that the Radon-Nikodym derivative of the law of the spatial increments (with endpoints away from the origin) of inhomogeneous Brownian last passage percolation (LPP) with n…
Coalescence of Geodesics in Exactly Solvable Models of Last Passage Percolation
Riddhipratim Basu, Sourav Sarkar, Allan Sly
Coalescence of semi-infinite geodesics remains a central question in planar first passage percolation. In this paper we study finer properties of the coalescence structure of finit…