Electronic Journal of Probability
- Electron. J. Probab.
- Volume 22 (2017), paper no. 13, 49 pp.
Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
We consider directed polymer models involving multiple non-intersecting random walks moving through a space-time disordered environment in one spatial dimension. For a single random walk, Alberts, Khanin and Quastel proved that under intermediate disorder scaling (in which time and space are scaled diffusively, and the strength of the environment is scaled to zero in a critical manner) the polymer partition function converges to the solution to the stochastic heat equation with multiplicative white noise. In this paper we prove the analogous result for multiple non-intersecting random walks started and ended grouped together. The limiting object now is the multi-layer extension of the stochastic heat equation introduced by O’Connell and Warren.
Electron. J. Probab., Volume 22 (2017), paper no. 13, 49 pp.
Received: 18 January 2017
Accepted: 29 January 2017
First available in Project Euclid: 3 February 2017
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Corwin, Ivan; Nica, Mihai. Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation. Electron. J. Probab. 22 (2017), paper no. 13, 49 pp. doi:10.1214/17-EJP32. https://projecteuclid.org/euclid.ejp/1486090893