Title   name
2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability
  Speaker   Sun, Rongfeng    
  Date 2018-11-15
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.
Abstract : The partition function of the directed polymer model on Z^{2+1} has been shown to undergo a phase transition on an intermediate disorder scale. In this talk, we focus on a window around the critical point. Exploiting a renewal process representation, we identify the asymptotics for the second and third moments of the partition function. As a corollary, we show that, viewed as a random field, the family of partition functions admits non-trivial diffusive scaling limits, and each limit point has the same covariance structure with logarithmic divergence near the diagonal. Similar results are obtained for the stochastic heat equation on R^2, extending earlier results by Bertini and Cancrini (98). Based on joint work with F. Caravenna and N. Zygouras.