Percolation in majority dynamics

Amir, Gideon; Baldasso, Rangel

doi:10.1214/20-ejp414

Cited by 5 publications

(1 citation statement)

References 19 publications

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“…In contrast to classical dynamical Bernoulli percolation, at any fixed time t ∈ (0, 1], the model exhibits dependencies of all orders. Other examples of models with infinite range dependence include Voronoi percolation [4], Boolean percolation [1], and Majority percolation [2]. In such models, a decoupling technique must be carried out to understand the underlying structure of the model.…”

Section: Introductionmentioning

confidence: 99%

Constrained-degree percolation in random environment

Sanchis¹,

Santos²,

Silva³

2020

Preprint

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We consider the Constrained-degree percolation model with random constraints on the square lattice and prove a non-trivial phase transition. In this model, each vertex has an independently distributed random constraint j ∈ {0, 1, 2, 3} with probability ρ j . Each edge e tries to open at a random uniform time U e , independently of all other edges. It succeeds if at time U e both its end-vertices have degrees strictly smaller than their respectively attached constraints. We show that this model undergoes a non-trivial phase transition when ρ 3 is sufficiently large. The proof consists of a decoupling inequality, the continuity of the probability for local events, together with a coarse-graining argument.

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Section: Introductionmentioning

confidence: 99%

Constrained-degree percolation in random environment

Sanchis¹,

Santos²,

Silva³

2020

Preprint

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Majority dynamics and the median process: Connections, convergence and some new conjectures

Amir

Baldasso

Nissan

2023

Stochastic Processes and their Applications

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Exponential decay for constrained-degree percolation

dos Santos,

Silva

2024

J. Appl. Probab.

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We consider the constrained-degree percolation model in a random environment (CDPRE) on the square lattice. In this model, each vertex v has an independent random constraint $\kappa_v$ which takes the value $j\in \{0,1,2,3\}$ with probability $\rho_j$ . The dynamics is as follows: at time $t=0$ all edges are closed; each edge e attempts to open at a random time $U(e)\sim \mathrm{U}(0,1]$ , independently of all the other edges. It succeeds if at time U(e) both its end vertices have degrees strictly smaller than their respective constraints. We obtain exponential decay of the radius of the open cluster of the origin at all times when its expected size is finite. Since CDPRE is dominated by Bernoulli percolation, this result is meaningful only if the supremum of all values of t for which the expected size of the open cluster of the origin is finite is larger than $\frac12$ . We prove this last fact by showing a sharp phase transition for an intermediate model.

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Percolation in majority dynamics

Cited by 5 publications

References 19 publications

Constrained-degree percolation in random environment

Constrained-degree percolation in random environment

Majority dynamics and the median process: Connections, convergence and some new conjectures

Exponential decay for constrained-degree percolation

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