8 papers
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…
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…
A New Outlook on the Profitability of Rogue Mining Strategies in the Bitcoin Network
Pantelis Tassopoulos, Yorgos Protonotarios
Many of the recent works on the profitability of rogue mining strategies hinge on a parameter called that measures the proportion of the honest network attracted by the attacke…
Brownian Motion & The Stochastic Behaviour of Stocks
Yorgos Protonotarios, Pantelis Tassopoulos
We begin by exploring the intuition of Brownian motion by explaining its birth through the observations of Robert Brown and later through Bachelier's work on its applications to th…