Electronic Journal of Probability

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

Ivan Corwin and Mihai Nica

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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

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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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 82C05: Classical dynamic and nonequilibrium statistical mechanics (general)

directed polymers stochastic heat equation KPZ scaling limits partition function non-intersecting processes

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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

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