87 citations · 243 across the 20 of their papers we have counts for
24 papers
The extreme statistics of some noncolliding Brownian processes
Mustazee Rahman
We consider certain noncolliding interacting particle systems driven by Brownian noise. A key example is drifted Brownian motions conditioned not to intersect and related models of…
Revisiting the temporal law in KPZ random growth
Mustazee Rahman
This article studies the temporal law of the KPZ fixed point. For the stationary geometry, we find the two-time law, which extends the single time law due to Baik-Rains and Ferrari…
The directed landscape seen from its trees
Mustazee Rahman, Balint Virag
A basic question about the directed landscape is how much of it can be reconstructed simply by knowing the shapes of its geodesics. We prove that the directed landscape can be reco…
On the duality between particles and polymers
Mustazee Rahman
We explore the connection between tasep-like interacting particle systems and last passage percolation type polymer models, focusing on three models: Geometric, Exponential and Bro…
Infinite geodesics, competition interfaces and the second class particle in the scaling limit
Mustazee Rahman, Balint Virag
We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish…
On inhomogeneous polynuclear growth
Kurt Johansson, Mustazee Rahman
This article studies the inhomogeneous geometric polynuclear growth model, the distribution of which is related to Schur functions. We explain a method to derive its distribution f…