## Electronic Journal of Probability

### Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 13, 49 pp.

Dates
Accepted: 29 January 2017
First available in Project Euclid: 3 February 2017

https://projecteuclid.org/euclid.ejp/1486090893

Digital Object Identifier
doi:10.1214/17-EJP32

Mathematical Reviews number (MathSciNet)
MR3613706

Zentralblatt MATH identifier
1357.60107

#### Citation

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

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