Universality in marginally relevant disordered systems (Q1688026)

A new approach is developed to investigate the continuum limit of marginality relevant systems of directed polymer type, which include the usual short-range directed polymer model on \(\mathbb Z^2\), the pinning model with tail exponent equal to \(1/2\) and long-range directed polymer model on \(\mathbb Z\) with Cauchy tails. It is shown that there is a common underlying structure among all these marginality relevant models which leads to a number of universal phenomena.