[en] We study the 2d directed polymer in random environment in a novel
*quasi-critical regime*, which interpolates between the much studied
sub-critical and critical regimes. We prove Edwards-Wilkinson fluctuations
throughout the quasi-critical regime, showing that the diffusively rescaled
partition functions are asymptotically Gaussian, under a rescaling which
diverges arbitrarily slowly as criticality is approached. A key challenge is
the lack of hypercontractivity, which we overcome deriving new sharp moment
estimates.
Disciplines :
Mathematics
Author, co-author :
Caravenna, Francesco
COTTINI, Francesca ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
ROSSI, Maurizia ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Mathematics
Language :
English
Title :
Quasi-critical fluctuations for 2d directed polymers
