Nikolaos Zygoras: Random polymers and their fluctuations

Random polymers describe a class of random walks in a random potential. Their partition function can be viewed as a discretisation of the solution to the stochastic heat equation and its logarithm (via the Hopf-Cole transform) as a discretisation of the solution to the KPZ equation. The KPZ equation has been proposed as a model for the universal fluctuations of stochastic growth models and in 1+1 dimensions the fluctuations of its solution is governed by a t^1/3 law. Under these lenses, I will review some of the current status of the fluctuation studies in random polymers.