Abstract
One way of approaching the question of the KPZ equation is to consider the problem of directed polymers in a random medium, which can be treated by the replica method. In dimension 1 + 1 and in its continuous version in time and space, this problem reduces to the study of a gas of delta-interacting bosons, a problem that Lieb and Liniger solved in the 1960s. The difficulty to overcome is that, in order to find the polymer free energy distribution, i.e. the height in the KPZ equation, by the replica method, it must be possible to make sense of a gas of bosons with a non-integer number of particles. Describing the technical aspects used to solve this difficulty, Pierre Le Doussal explained how this replica approach to the KPZ equation enables us to recover the Tracy Widom distribution.
