Browsing by Author "Saglietti, Santiago"

Now showing 1 - 4 of 4
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    A non-oriented first passage percolation model and statistical invariance by time reversal
    (2024) Ramirez, Alejandro F.; Saglietti, Santiago; Shao, Lingyun
    We introduce and study a non -oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of outgoing edges from a given vertex are distributed according to a generalized Bernoulli-Exponential law and i.i.d. among vertices. We derive the statistical invariance property by time reversal through a zero -temperature limit of the random walk in Dirichlet environment model.
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    QUENCHED AND AVERAGED LARGE DEVIATIONS FOR RANDOM WALKS IN RANDOM ENVIRONMENTS: THE IMPACT OF DISORDER
    (2023) Bazaes, Rodrigo; Mukherjee, Chiranjib; Ramirez, Alejandro F.; Saglietti, Santiago
    In 2003, Varadhan (Comm. Pure Appl. Math. 56 (2003) 1222-1245) de-veloped a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on Zd. One fundamental question which remained open was to determine when the quenched and averaged large deviation rate functions agree, and when they do not. In this article we show that for RWRE in uniformly elliptic and i.i.d. environment in d > 4, the two rate functions agree on any compact set contained in the interior of their domain which does not contain the origin, provided that the disorder of the environment is sufficiently low. Our result provides a new formulation which encompasses a set of sufficient conditions under which these rate functions agree without assuming that the RWRE is ballistic (see (Probab. Theory Related Fields 149 (2011) 463-491)), satis-fies a CLT or even a law of large numbers (Electron. Commun. Probab. 7 (2002)191-197; Ann. Probab. 36 (2008) 728-738). Also, the equality of rate functions is not restricted to neighborhoods around given points, as long as the disorder of the environment is kept low. One of the novelties of our ap-proach is the introduction of an auxiliary random walk in a deterministic envi-ronment which is itself ballistic (regardless of the actual RWRE behavior) and whose large deviation properties approximate those of the original RWRE in a robust manner, even if the original RWRE is not ballistic itself.
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    SCALING LIMIT OF THE HEAVY TAILED BALLISTIC DEPOSITION MODEL WITH p-STICKING
    (2023) Comets, Francis; Dalmau, Joseba; Saglietti, Santiago
    Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of Z and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. and heavy tailed, and where each block sticks to the interface at the first point of contact with probability p (otherwise, it falls straight down until it lands on a block belonging to the interface). We study scaling limits of the resulting interface for the different values of p and show that there is a phase transition as p goes from 1 to 0.
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    The effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior
    (2023) Bazaes, Rodrigo; Mukherjee, Chiranjib; Ramirez, Alejandro F.; Saglietti, Santiago
    For 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.