The effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior

Simple item page
dc.contributor.authorBazaes, Rodrigo
dc.contributor.authorMukherjee, Chiranjib
dc.contributor.authorRamirez, Alejandro F.
dc.contributor.authorSaglietti, Santiago
dc.date.accessioned2025-01-20T20:15:48Z
dc.date.available2025-01-20T20:15:48Z
dc.date.issued2023
dc.description.abstractFor a random walk in a uniformly elliptic and i.i.d. environment on Zd with d >= 4, we show that the quenched and annealed large deviation rate functions agree on any compact set contained in the boundary an := {x is an element of Rd : |x|1 = 1} of their domain which does not intersect any of the (d - 2)-dimensional facets of an, provided that the disorder of the environment is low enough (depending on the compact set). As a consequence, we obtain a simple explicit formula for both rate functions on any such compact set of an at low enough disorder. In contrast to previous works, our results do not assume any ballistic behavior of the random walk and are not restricted to neighborhoods of any given point (on the boundary an). In addition, our results complement those in Bazaes et al. (2022), where, using different methods, we investigate the equality of the rate functions in the interior of their domain. Finally, for a general parametrized family of environments, we show that the strength of disorder determines a phase transition in the equality of both rate functions, in the sense that for each x is an element of an there exists ex such that the two rate functions agree at x when the disorder is smaller than ex and disagree when it is larger. This further reconfirms the idea, introduced in Bazaes et al. (2022), that the disorder of the environment is in general intimately related with the equality of the rate functions.(c) 2023 Elsevier B.V. All rights reserved.
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.spa.2023.01.003
dc.identifier.eissn1879-209X
dc.identifier.issn0304-4149
dc.identifier.urihttps://doi.org/10.1016/j.spa.2023.01.003
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/92285
dc.identifier.wosidWOS:000960952900001
dc.language.isoen
dc.pagina.final237
dc.pagina.inicio208
dc.revistaStochastic processes and their applications
dc.rightsacceso restringido
dc.subjectrandom walk in random environment
dc.subjectlarge deviations
dc.titleThe effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior
dc.typeartículo
dc.volumen158
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
Files
Collections
Artículos de revistas