An exact solution for the KPZ equation with flat initial conditions

Understand

We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum KPZ growth equation in one dimension with flat initial conditions.

• We use the mapping onto a directed polymer (DP) with one end fixed, one free, and the Bethe Ansatz for the replicated attractive boson model.
• We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian.
• Our formula, valid for all times, exhibits convergence of the free energy (i.e.