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2015 Directed polymers in a random environment with a defect line
Kenneth Alexander, Gökhan Yıldırım
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Electron. J. Probab. 20: 1-20 (2015). DOI: 10.1214/EJP.v20-3379


We study the depinning transition of the $1+1$ dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site of $\mathbb{Z}^2$; sites on the positive axis have the potential enhanced by a deterministic value $u$. We show that for small inverse temperature $\beta$ the quenched and annealed free energies differ significantly at most in a small neighborhood (of size of order $\beta$) of the annealed critical point $u_c^a=0$. For the case $u=0$, we show that the difference between quenched and annealed free energies is of order $\beta^4$ as $\beta\to 0$, assuming only finiteness of exponential moments of the potential values, improving existing results which required stronger assumptions.


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Kenneth Alexander. Gökhan Yıldırım. "Directed polymers in a random environment with a defect line." Electron. J. Probab. 20 1 - 20, 2015.


Accepted: 22 January 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1308.82038
MathSciNet: MR3311219
Digital Object Identifier: 10.1214/EJP.v20-3379

Primary: 82B44
Secondary: 60K35 , 82D60

Keywords: Depinning transition , Lipschitz percolation , Pinning , Random walk


Vol.20 • 2015
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