5 papers · 1 filter
Bi-infinite systems of singularly interacting Brownian particles and the KPZ equation
Sayan Banerjee, Amarjit Budhiraja, Peter Rudzis
We study a bi-infinite system of interacting Brownian particles on the real line with singular asymmetric interactions mediated by the collision local times. Particles perform Brow…
Long Time Asymptotics for the Stochastic Follow-the-Leader System
Sayan Banerjee, Amarjit Budhiraja, Dilshad Imon
We introduce and analyze a class of interacting particle systems on the real line that combine features of the stochastic rat race and (deterministic) follow-the-leader models. The…
Strong existence, pathwise uniqueness and chains of collisions in infinite Brownian particle systems
Sayan Banerjee, Amarjit Budhiraja, Peter Rudzis
We study strong existence and pathwise uniqueness for a class of infinite-dimensional singular stochastic differential equations (SDE), with state space as the cone $\{x \in \mathb…
Flocking under Fast and Large Jumps: Stability, Chaos, and Traveling Waves
Sayan Banerjee, Amarjit Budhiraja, Dilshad Imon
We study a model for flocking given by a -particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution , with r…
Fluctuations of the Atlas model from inhomogeneous stationary profiles
Sayan Banerjee, Amarjit Budhiraja, Peter Rudzis
The infinite Atlas model describes the evolution of a countable collection of Brownian particles on the real line, where the lowest particle is given a drift of .…