### Speaker

### Description

The KPZ equation[1] is connected to a large number of processes, such as atomic deposition, evolution of bacterial colonies, the direct polymer model, the weakly asymmetric simple exclusion process, the totally asymmetric exclusion process, direct d-mer diffusion, fire propagation, turbulent liquid-crystal, spin dynamics, polymer deposition in semiconductors, and etching [2]. We present a short review of the field, some modern problems and perspectives. We discuss as well how a new interpretation of the fluctuation-dissipation theorem[3] allows us to give a solution for the KPZ exponents[4].

References

[1] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. {\bf 56}, 9, 889 (1986).

[2] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. Rev. E \textbf{63}, 041113 (2001).

--- E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. Phys. A {\bf 48}, 035001 (2015).

--- W. R. Gomes, A. L. A. Penna and F. A. Oliveira, Phys. Rev. E \textbf{100} 02101 (2019)

[3] M. S. Gomes-Filho, and F. A. Oliveira, EPL \textbf{133} 10001 (2021) --- P. R. H. dos Anjos, W. S. Alves, M. S. Gomes-Filho, D. L. Azevedo and F. A. Oliveira, Frontiers in Physics 9 (https://doi.org/10.3389/fphy.2021.741590), 741590 (2021).

[4] M. S. Gomes-Filho, A. L. A. Penna and F. A. Oliveira, Results in Physics 26, \textbf{26} 104435 (2021).