Sharp threshold for two-dimensional majority dynamics percolation

Caio Alves, Rangel Baldasso

Research output: Contribution to journalArticlepeer-review

Abstract

In this work we consider the two-dimensional percolation model arising from the majority dynamics process at a given time t ∈ ℝ+. We show the emergence of a sharp threshold phenomenon for the box crossing event at the critical probability parameter pc(t) with polynomial size window. We then use this result in order to obtain stretched-exponential bounds on the one-arm event probability in the subcritical phase. Our results are based on differential inequalities derived from the OSSS inequality, inspired by the recent developments by Ahlberg, Broman, Griffiths, and Morris and by Duminil-Copin, Raoufi, and Tassion. We also provide analogous results for percolation in the voter model.

Original languageEnglish
Pages (from-to)1869-1886
Number of pages18
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume58
Issue number4
DOIs
StatePublished - Nov 2022
Externally publishedYes

Funding

CA is supported by the DFG grant SA 3465/1-1. RB is supported by the Israel Science Foundation through grant 575/16 and by the German Israeli Foundation through grant I-1363-304.6/2016.

FundersFunder number
German Israeli FoundationI-1363-304.6/2016
Deutsche ForschungsgemeinschaftSA 3465/1-1
Israel Science Foundation575/16

    Keywords

    • Opinion dynamics
    • Percolation
    • Sharp thresholds

    Fingerprint

    Dive into the research topics of 'Sharp threshold for two-dimensional majority dynamics percolation'. Together they form a unique fingerprint.

    Cite this