## Another look at the Balázs-Quastel-Seppäläinen theorem

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- by Yu Gu and Tomasz Komorowski;
- Trans. Amer. Math. Soc.
**376**(2023), 2947-2962 - DOI: https://doi.org/10.1090/tran/8847
- Published electronically: January 12, 2023
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## Abstract:

We study the KPZ equation with a $1+1-$dimensional spacetime white noise, started at equilibrium, and give a different proof of the main result of Balázs, Quastel, and Seppäläinen [J. Amer. Math. Soc. 24 (2011), pp. 683–708], i.e., the variance of the solution at time $t$ is of order $t^{2/3}$. Instead of using a discrete approximation through the exclusion process and the second class particle, we utilize the connection to directed polymers in random environment. Along the way, we show the annealed density of the stationary continuum directed polymer equals to the two-point covariance function of the stationary stochastic Burgers equation, confirming the physics prediction of Maes and Thiery [J. Stat. Phys. 168 (2017), pp. 937–963].## References

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## Bibliographic Information

**Yu Gu**- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
**Tomasz Komorowski**- Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656, Warsaw, Poland
- MR Author ID: 307391
- ORCID: 0000-0003-1564-0169
- Received by editor(s): March 9, 2022
- Received by editor(s) in revised form: September 23, 2022
- Published electronically: January 12, 2023
- Additional Notes: The first author was partially supported by the NSF through DMS-2203014. The second author was supported by NCN grant 2020/37/B/ST1/00426.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**376**(2023), 2947-2962 - MSC (2000): Primary 35R60, 60H07, 60H15
- DOI: https://doi.org/10.1090/tran/8847
- MathSciNet review: 4557886