Pantelis Tassopoulos

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20212026

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math.PR2026

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…

math.PR2026

The starting point of a directed geodesic is special

Pantelis Tassopoulos, Sourav Sarkar

For any $t \in [0, 1/2)$ , consider the process $η_{t} : [0, 1/2] \mapsto R$ defined by $η_{t} (s) = Π (t + s) - Π (t)$ , where $Π$ is the directed geodesic from $(0, 0)$ to $(0, 1)$ in the direc…

math.PR2026

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…

math.PR2025

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…

math.PR2025

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…

math.PR2024

The KPZ Fixed Point and the Directed Landscape

Pantelis Tassopoulos

The term 'KPZ' stands for the initials of three physicists, namely Kardar, Parisi and Zhang, which, in 1986 conjectured the existence of universal scaling behaviours for many rando…