Translator Disclaimer
2017 Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation
Ivan Corwin, Mihai Nica
Electron. J. Probab. 22: 1-49 (2017). DOI: 10.1214/17-EJP32

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.

Citation

Download Citation

Ivan Corwin. Mihai Nica. "Intermediate disorder directed polymers and the multi-layer extension of the stochastic heat equation." Electron. J. Probab. 22 1 - 49, 2017. https://doi.org/10.1214/17-EJP32

Information

Received: 18 January 2017; Accepted: 29 January 2017; Published: 2017
First available in Project Euclid: 3 February 2017

zbMATH: 1357.60107
MathSciNet: MR3613706
Digital Object Identifier: 10.1214/17-EJP32

Subjects:
Primary: 60F05, 82C05

JOURNAL ARTICLE
49 PAGES


SHARE
Vol.22 • 2017
Back to Top