Pathways Workshop: Kinetic Theory & Stochastic Partial Differential Equations: Viscous shock solutions in KPZ
Presenter
August 21, 2025
Keywords:
- singular SPDEs
- regularity structures
- paracontrolled calculus
- KPZ equation
- space-time white noise
- stochastic quantization
- Multiscale analysis
- Intermittency
- SPDEs from fluid dynamics
- Boltzmann equation
- Vlasov-Poisson system
- Vlasov-Maxwell system
- Fokker-Planck equation
- BBGKY hierarchy
MSC:
- 60H15 - Stochastic partial differential equations (aspects of stochastic analysis) [See also 35R60]
- 82C40 - Kinetic theory of gases in time-dependent statistical mechanics
Abstract
I will present some joint work with Evan Sorensen on the long-term behavior of "V-shaped" solutions for the KPZ equation and the KPZ fixed point, and describe how this understanding can be used in the classification of time-invariant measures for this equation. I will also describe the relationship between these solutions and shock solutions for the stochastic Burgers equation.