5 papers
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 , and are supported…
The discrete periodic Pitman transform: invariances, braid relations, and Burke properties
Eva R. Engel, Benjamin Jasper Kra-Caskey, Oleksandr Lazorenko +5
We develop the theory of the discrete periodic Pitman transform, first introduced by Corwin, Gu, and the fifth author. We prove that the discrete periodic Pitman transform satisfie…
Viscous shock fluctuations in KPZ
Alexander Dunlap, Evan Sorensen
We study ``V-shaped'' solutions to the KPZ equation, those having opposite asymptotic slopes and , with , at positive and negative infinity, respectively. Answering…
Periodic Pitman transforms and jointly invariant measures
Ivan Corwin, Yu Gu, Evan Sorensen
We construct explicit jointly invariant measures for the periodic KPZ equation (and therefore also the stochastic Burgers' and stochastic heat equations) for general slope paramete…
Exceptional force, uncountably many solutions in the KPZ fixed point
Sudeshna Bhattacharjee, Ofer Busani, Evan Sorensen
We give a complete characterization of all eternal solutions of the KPZ fixed point satisfying the asymptotic slope condition $\lim_{|x| \to \infty} \frac{b(x,0)}{x} = 2ξ…