Integrable Fluctuations in One-Dimensional Random Growth

Explore the fascinating world of asymptotic fluctuations in the KPZ universality class through this 46-minute lecture by Daniel Remenik. Delve into a broad collection of probabilistic models, including one-dimensional random growth, directed polymers, and particle systems. Discover the remarkable solvability of these models and learn about explicit formulas for their transition probabilities. Examine the KPZ fixed point, a scaling invariant Markov process that emerges as the scaling limit for all models in the class. Investigate how the transition probabilities of these processes satisfy classical integrable differential equations. Follow the lecture's progression from an introduction to the KPZ universality conjecture through to the polynuclear growth process, integrability of the KPZ fixed point, and the PNG Fredholm determinant formula. Gain insights into droplet/narrow wedge initial conditions and the scaling limit of discrete time TASEP with parallel updates.

Intro
Outline
KPZ universality conjecture
The polynuclear growth process (PNG)
Droplet/narrow wedge initial condition
Integrability of the KPZ fixed point
PNG Fredholm determinant formula
The formula was first obtained as the scaling limit of a similar formula for discrete time TASEP with parallel
KPZ fixed point formula