The heat and the landscape I

Understand

Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape.

• In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ fixed point.
• The key is that one-dimensional Baik-Ben Arous-Peche statistics characterize the KPZ fixed point.
• This yields a general and elementary method that shows convergence based on previously established limit theorems.