Abstract
We prove that the Beta random walk, introduced in [BC17] 2017, has cubic fluctuations from the large deviation principle of the GUE Tracy-Widom type for arbitrary values and of the parameters of the Beta distribution, removing previous restrictions on their values. Furthermore, we prove that the GUE Tracy-Widom fluctuations still hold in the intermediate disorder regime. We also show that any random walk in space-time random environment that matches certain moments with the Beta random walk also has GUE Tracy-Widom fluctuations in the intermediate disorder regime. As a corollary we show the emergence of GUE Tracy-Widom fluctuations from the large deviation principle for trajectories ending at boundary points for random walks in space (time-independent) i.i.d. Dirichlet random environment in dimension for a class of asymptotic behavior of the parameters.
Funding Statement
Alejandro F. Ramírez has been partially supported by Iniciativa Científica Milenio and by Fondo Nacional de Desarrollo Científico y Tecnológico grant 1180259 and 1220396.
Acknowledgments
Alejandro F. Ramírez is grateful to José A. Ramírez for useful discussions.
Citation
Giancarlos Oviedo. Gonzalo Panizo. Alejandro F. Ramírez. "Second order cubic corrections of large deviations for perturbed random walks." Electron. J. Probab. 27 1 - 45, 2022. https://doi.org/10.1214/22-EJP786
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