Department of

August 2014 September 2014 October 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 1 2 3 4 5 6 1 2 3 4 3 4 5 6 7 8 9 7 8 9 10 11 12 13 5 6 7 8 9 10 11 10 11 12 13 14 15 16 14 15 16 17 18 19 20 12 13 14 15 16 17 18 17 18 19 20 21 22 23 21 22 23 24 25 26 27 19 20 21 22 23 24 25 24 25 26 27 28 29 30 28 29 30 26 27 28 29 30 31 31

Tuesday, September 9, 2014

**Abstract:** The directed polymer model at intermediate disorder regime was introduced by Alberts-Khanin-Quastel in 2012. It was proved that at inverse temperature $\beta n^{-\gamma}$ with $\gamma=1/4$ the partition function, centered appropriately, converges in distribution and the limit is given in terms of the solution of the stochastic heat equation. This result was obtained under the assumption that the disorder variables posses exponential moments, but its universality was also conjectured under the assumption of six moments. We show that this conjecture is valid and we further extend it by exhibiting the non-universal limiting behavior in the case of less than six moments. We also explain the behavior of the scaling exponent for the log-partition function under different moment assumptions and values of $\gamma$. Based on joint work with Nikos Zygouras.

Tuesday, September 16, 2014

Tuesday, September 23, 2014

Tuesday, September 30, 2014

Wednesday, October 1, 2014

Tuesday, October 14, 2014

Tuesday, October 21, 2014

Tuesday, October 28, 2014