IS31: Random Growth and KPZ Universality

Organizer: Shirshendu Ganguly (UC Berkeley)

Scaling limit of half-space KPZ equation

Sayan Das

We consider the KPZ equation in the half-space: \[\partial_t\mathcal{H} = \frac12\partial_x^2\mathcal{H}+\frac12(\partial_x \mathcal{H})^2+\xi, \quad (x,t)\in \mathbb{R}_{\ge0}^2\] with narrow wedge initial data and Neumann boundary condition: \[\partial_x\mathcal{H}(x,t)\mid_{x=0}=\alpha\] In the talk, I will discuss the process level scaling limit of \(\mathcal{H}(x,t)\) as \(t\to \infty\) under the 1:2:3 KPZ scaling. This is based on a joint work with Christian Serio.