The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations Abstract:
I will describe a series of work, joint with Francesco Caravenna and Rongfeng Sun, which make some first steps towards the understanding of scaling limits of disordered systems in a suitable
weak disorder regime, where disorder has a so-called marginally relevant effect. This includes some first understanding of the KPZ equation in two space dimensions, which in the language of SPDEs
is the \critical dimension". Among the results that we will describe is a phase transition and the identification of the KPZ solution below a critical temperature, which falls into the Edwards-Wilkinson universality class. Emphasis will be given on the methods which include Lindeberg principles, fourth moment theorems, analysis on Wiener spaces, multiscale analysis etc.
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