Lower large deviations for the maximal flow through a domain of $${\mathbb{R}^d}$$ in first passage percolation - Archive ouverte HAL Access content directly
Journal Articles Probability Theory and Related Fields Year : 2011

Lower large deviations for the maximal flow through a domain of $${\mathbb{R}^d}$$ in first passage percolation

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Raphaël Cerf
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  • PersonId : 955337
Marie Théret
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  • PersonId : 1188275

Abstract

We consider the standard first passage percolation model in the rescaled graph Z d /n for d ≥ 2, and a domain Ω of boundary Γ in R d. Let Γ 1 and Γ 2 be two disjoint open subsets of Γ, representing the parts of Γ through which some water can enter and escape from Ω. We investigate the asymptotic behaviour of the flow φ n through a discrete version Ω n of Ω between the corresponding discrete sets Γ 1 n and Γ 2 n. We prove that under some conditions on the regularity of the domain and on the law of the capacity of the edges, the lower large deviations of φ n /n d−1 below a certain constant are of surface order.
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Dates and versions

hal-03856495 , version 1 (16-11-2022)

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Raphaël Cerf, Marie Théret. Lower large deviations for the maximal flow through a domain of $${\mathbb{R}^d}$$ in first passage percolation. Probability Theory and Related Fields, 2011, 150 (3-4), pp.635-661. ⟨10.1007/s00440-010-0287-6⟩. ⟨hal-03856495⟩
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