SPMES: The Positive Rates Conjecture in Nearest-Neighbor Cellular Automata - Georg Menz

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  • Опубліковано 18 гру 2024
  • Seminário de Probabilidade e Mecânica Estatística
    Título: The Positive Rates Conjecture in Nearest-Neighbor Cellular Automata
    Palestrante: Georg Menz, UCLA
    Playlist dos videos: bit.ly/30ZkHWe
    Resumo: A cellular automaton describes a process in which cells evolve according to a set of rules. Which rule is applied to a specific cell only depends on the states of the neighboring and the cell itself. Considering a one-dimensional cellular automaton with finite range, the positive rates conjecture states that and under the presence of noise the associated stationary measure must be unique. We restrict ourselves to the case of nearest-neighbor interaction where simulations suggest that the positive rates conjecture is true. After discussing a simple criterion to deduce decay of correlations, we show that the positive rates conjecture is true for almost all nearest-neighbor cellular automatons. The main tool is comparing a one-dimensional cellular automaton to a properly chosen two-dimensional Ising-model. We outline a pathway to resolve the remaining open cases. This presentation is based on collaborative work with Maciej Gluchowski from the University of Warsaw and Jacob Manaker from UCLA
    Apoio:
    IMPA
    Instituto Superior Técnico de Lisboa
    UFBA
    UFMG
    UFRGS
    UFRJ
    Unicamp
    Universidade do Porto
    USP
    Comitê científico:
    Luiz Renato Fontes (USP)
    Tertuliano Franco (UFBA)
    Nancy Lopes Garcia (Unicamp)
    Patrícia Gonçalves (IST, Lisboa)
    Marcelo Hilário (UFMG)
    Roberto Imbuzeiro (Coordenador, IMPA)
    Claudio Landim (Coordenador, IMPA)
    Adriana Neumann (UFRGS)
    Serguei Popov (UP, Porto)
    Glauco Valle (UFRJ)
    Redes Sociais do IMPA: linktr.ee/impabr
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