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Moment Asymptotics for the (2+1)-dimensional Directed Polymer in the Critical Window
[2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability]
Date: 2018-11-15
Speaker : Sun, Rongfeng (NUS)
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.
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