Mathematics – Probability
Scientific paper
2012-02-20
Mathematics
Probability
38 pages
Scientific paper
We introduce a new disorder regime for directed polymers in dimension 1+1 that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter beta to zero as the polymer length n tends to infinity. The natural choice of scaling is beta*n^{-1/4}. We show that the polymer measure under this scaling has previously unseen behavior. While the fluctuation exponents of the polymer endpoint and the log partition function are identical to those for simple random walk (zeta = 1/2, chi = 0), the fluctuations themselves are different. These fluctuations are still influenced by the random environment and there is no self-averaging of the polymer measure. In particular, the random distribution of the polymer endpoint converges in law (under a diffusive scaling of space) to a random absolutely continuous measure on the real line. The randomness of the measure is inherited from a stationary process A_{beta} that has the recently discovered crossover distributions as its one-point marginals. We also prove existence of a limiting law for the four-parameter field of polymer transition probabilities. The limit can be described by the stochastic heat equation.
Alberts Tom
Khanin Konstantin
Quastel Jeremy
No associations
LandOfFree
The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Intermediate Disorder Regime for Directed Polymers in Dimension 1+1 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565588