Stochastic telegraph equation limit for the stochastic six vertex model
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- by Hao Shen and Li-Cheng Tsai
- Proc. Amer. Math. Soc. 147 (2019), 2685-2705
- DOI: https://doi.org/10.1090/proc/14415
- Published electronically: March 1, 2019
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Abstract:
In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin, where the weights of corner-shape vertices are tuned to zero, and prove their conjecture that the height fluctuation converges in finite dimensional distributions to the solution of the stochastic telegraph equation.References
- A. Aggarwal and A. Borodin, Phase transitions in the ASEP and stochastic six-vertex model, arXiv:1607.08684, 2016.
- Amol Aggarwal, Current fluctuations of the stationary ASEP and six-vertex model, Duke Math. J. 167 (2018), no. 2, 269–384. MR 3754630, DOI 10.1215/00127094-2017-0029
- Guillaume Barraquand, Alexei Borodin, Ivan Corwin, and Michael Wheeler, Stochastic six-vertex model in a half-quadrant and half-line open asymmetric simple exclusion process, Duke Math. J. 167 (2018), no. 13, 2457–2529. MR 3855355, DOI 10.1215/00127094-2018-0019
- Alexei Borodin, Ivan Corwin, and Vadim Gorin, Stochastic six-vertex model, Duke Math. J. 165 (2016), no. 3, 563–624. MR 3466163, DOI 10.1215/00127094-3166843
- A. Borodin and V. Gorin, A stochastic telegraph equation from the six-vertex model, arXiv:1803.09137, 2018.
- Alexei Borodin and Grigori Olshanski, The ASEP and determinantal point processes, Comm. Math. Phys. 353 (2017), no. 2, 853–903. MR 3649488, DOI 10.1007/s00220-017-2858-1
- Alexei Borodin and Leonid Petrov, Higher spin six vertex model and symmetric rational functions, Selecta Math. (N.S.) 24 (2018), no. 2, 751–874. MR 3782413, DOI 10.1007/s00029-016-0301-7
- I. Corwin, P. Ghosal, H. Shen, and L.-C. Tsai, Stochastic pde limit of the six vertex model, preprint, arXiv:1803.08120, 2018.
- Ivan Corwin and Leonid Petrov, Stochastic higher spin vertex models on the line, Comm. Math. Phys. 343 (2016), no. 2, 651–700. MR 3477349, DOI 10.1007/s00220-015-2479-5
- Ivan Corwin and Li-Cheng Tsai, KPZ equation limit of higher-spin exclusion processes, Ann. Probab. 45 (2017), no. 3, 1771–1798. MR 3650415, DOI 10.1214/16-AOP1101
- Leh-Hun Gwa and Herbert Spohn, Six-vertex model, roughened surfaces, and an asymmetric spin Hamiltonian, Phys. Rev. Lett. 68 (1992), no. 6, 725–728. MR 1147356, DOI 10.1103/PhysRevLett.68.725
- P. Hall and C. C. Heyde, Martingale limit theory and its application, Probability and Mathematical Statistics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 624435
- Nicolai Reshetikhin and Ananth Sridhar, Limit shapes of the stochastic six vertex model, Comm. Math. Phys. 363 (2018), no. 3, 741–765. MR 3858820, DOI 10.1007/s00220-018-3253-2
Bibliographic Information
- Hao Shen
- Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
- MR Author ID: 1041376
- Email: pkushenhao@gmail.com
- Li-Cheng Tsai
- Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
- MR Author ID: 949011
- Email: lctsai.math@gmail.com
- Received by editor(s): July 14, 2018
- Received by editor(s) in revised form: September 24, 2018
- Published electronically: March 1, 2019
- Additional Notes: The first author was partially supported by the NSF through DMS:1712684.
The second author was partially supported by the NSF through DMS-1712575 and the Simons Foundation through a Junior Fellowship.
This work was initiated in the conference Integrable Probability Boston 2018, May 14-18, 2018, at MIT, which was supported by the NSF through DMS-1664531, DMS-1664617, DMS-1664619, and DMS-1664650. - Communicated by: Zhen-Qing Chen
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2685-2705
- MSC (2010): Primary 60H15, 82B20
- DOI: https://doi.org/10.1090/proc/14415
- MathSciNet review: 3951443