Abstract
In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aggarwal, A.: Current Fluctuations of the Stationary ASEP and Stochastic Six-Vertex Model. preprint, arXiv:1608.04726
Aggarwal, A., Borodin, A.: Phase Transitions in the ASEP and Stochastic Six-Vertex Model. preprint, arXiv:1607.08684
Balász, M., Seppäläinen, T.: Order of Current Variance and Diffusivity in the Asymmetric Simple Exclusion Process. Ann. Math. 171, 1237–1265 (2010)
Baxter, R.J.: Exactly Solved Models in Statistical Mechanics. Academic Press, London (1989)
van Beijern, H., Kutner, R., Spohn, H.: Excess Noise for Driven Diffusive Systems. Phys. Rev. Lett. 54, 2026–2029 (1985)
Borodin, A., Corwin, I., Gorin, V.: Stochastic Six-Vertex Model. Duke Math. J. 165, 563–624 (2016)
Borodin, A., Petrov, L.: Higher Spin Six-Vertex Models and Rational Symmetric Functions, To appear in Sel. Math. arXiv:1601.05770
Borodin, A., Petrov, L. preprint, arXiv:1605.01349
Corwin, I.: The Kardar-Parisi-Zhang Equation and Universality Class. Random Matrices Theory Appl., 1 (2012)
Ferrari, P.A., Fontes, L.R.G.: Current Fluctuations for the Asymmetric Simple Exclusion Process. Ann. Prob. 22, 820–832 (1994)
Gwa, L.-H., Spohn, H.: Six-Vertex Model, Roughened Surfaces, and an Asymmetric Spin Hamiltonian. Phys. Rev. Lett. 68, 725–728 (1992)
Harris, T.E.: Additive Set-Valued Markov Processes and Graphical Methods. Ann. Prob. 6, 355–378 (1978)
Harris, T.E.: Nearest-Neighbor Markov Interaction Processes on Multidimensional Lattices. Adv. Math. 9, 66–89 (1972)
Holley, R.: A Class of Interactions in an Infinite Particle System. Adv. Math. 5, 291–309 (1970)
Kardar, M., Parisi, G., Zhang, Y-C.: Dynamic Scaling of Growing Interfaces. Phys. Rev. Lett. 56, 889–892 (1986)
MacDonald, J., Gibbs, J., Pipkin, A.: Kinetics of Biopolymerization on Nucleic Acid Templates. Biopolymers 6, 1–25 (1968)
Lieb, E.H.: Residual Entropy of Square Ice. Phys. Rev. Lett. 162, 162–172 (1967)
Liggett, T.M.: Existence Theorems for Infinite Particle Systems. Trans. Amer. Math. Soc. 165, 481–481 (1972)
Spitzer, F.: Interaction of Markov Processes. Adv. Math. 5, 246–290 (1970)
Tracy, C.A., Widom, H.: A Fredholm Determinant Representation in ASEP. J. Stat. Phys. 132, 291–300 (2008)
Tracy, C.A., Widom, H.: Asymptotics in ASEP With Step Initial Condition. Comm. Math. Phys. 290, 129–154 (2009)
Tracy, C.A., Widom, H.: Integral Formulas for the Asymmetric Simple Exclusion Process. Comm. Math. Phys. 279, 815–844 (2008)
Tracy, C.A., Widom, H.: On ASEP With Step Bernoulli Initial Condition. J. Stat. Phys. 137, 825–838 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was funded by the Eric Cooper and Naomi Siegel Graduate Student Fellowship I and the NSF Graduate Research Fellowship under grant number DGE1144152.
Rights and permissions
About this article
Cite this article
Aggarwal, A. Convergence of the Stochastic Six-Vertex Model to the ASEP. Math Phys Anal Geom 20, 3 (2017). https://doi.org/10.1007/s11040-016-9235-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11040-016-9235-8