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math.PR2026
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…
math.PR2026
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…