Alexander Dunlap

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math.PR2025

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 $θ > 0$ , and are supported…

math.PR2024

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…

math.PR2024

Viscous shock fluctuations in KPZ

Alexander Dunlap, Evan Sorensen

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

math.PR2024

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…