Alexander Dunlap

collaborators

5 papers

math.PR2026

Invariant measures and shocks in the KPZ fixed point

Alexander Dunlap, Evan Sorensen

We construct a family of invariant measures from the perspective of a shock in the KPZ fixed point. These measures are parameterized by a positive number $I^¸ > 0$ , and are supported…

math.PR2025

Viscous shock fluctuations in KPZ

Alexander Dunlap, Evan Sorensen

We study ``V-shaped'' solutions to the KPZ equation, those having opposite asymptotic slopes $I^¸$ and $- I^¸$ , with $I^¸ > 0$ , at positive and negative infinity, respectively. Answering…

math.PR2025

Edwards-Wilkinson fluctuations in subcritical 2D stochastic heat equations

Alexander Dunlap, Cole Graham

We study 2D nonlinear stochastic heat equations under a logarithmically attenuated white-noise limit with subcritical coupling. We show that solutions asymptotically exhibit Edward…

math.PR2025

Additive-multiplicative stochastic heat equations, stationary solutions, and Cauchy statistics

Alexander Dunlap, Chiranjib Mukherjee

We study long-term behavior and stationary distributions for stochastic heat equations forced simultaneously by a multiplicative noise and an independent additive noise with the sa…

math.PR2025

Simultaneous global inviscid Burgers flows with periodic Poisson forcing

Alexander Dunlap

We study the inviscid Burgers equation on the circle $T := R / Z$ forced by the derivative of a Poisson point process on $R \times T$ . We con…