Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions

Gideon Amir, Ivan Corwin, Jeremy Quastel

We consider the solution of the stochastic heat equation \partial_T \mathcal{Z} = 1/2 \partial_X^2 \mathcal{Z} - \mathcal{Z} \dot{\mathscr{W}} with delta function initial condition…