Probability Surveys

On the scaling limits of weakly asymmetric bridges

Cyril Labbé

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Abstract

We consider a discrete bridge from $(0,0)$ to $(2N,0)$ evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order $N^{-\alpha}$ with $\alpha\in(0,\infty)$. We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter $\alpha$.

Article information

Source
Probab. Surveys, Volume 15 (2018), 156-242.

Dates
Received: May 2017
First available in Project Euclid: 20 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ps/1537408916

Digital Object Identifier
doi:10.1214/17-PS285

Mathematical Reviews number (MathSciNet)
MR3856167

Zentralblatt MATH identifier
06942908

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60H15: Stochastic partial differential equations [See also 35R60] 82C24: Interface problems; diffusion-limited aggregation

Keywords
Exclusion process height function bridge stochastic heat equation Burgers equation KPZ equation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Labbé, Cyril. On the scaling limits of weakly asymmetric bridges. Probab. Surveys 15 (2018), 156--242. doi:10.1214/17-PS285. https://projecteuclid.org/euclid.ps/1537408916


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References

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