Browsing by Author "Panizo, Gonzalo"

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    Second order cubic corrections of large deviations for perturbed random walks*
    (2022) Oviedo, Giancarlos; Panizo, Gonzalo; Ramirez, Alejandro F.
    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 ?? > 0 and (3 > 0 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 d = 2 for a class of asymptotic behavior of the parameters.