Product Type Potential on the One-Dimensional Lattice Systems: Selection of Maximizing Probability and a Large Deviation Principle

• J. Mohr ^[1]
  1. [1] UFRGS (Brasil)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Given an uncountable and compact metric space E, the one-dimensional lattice system is the space Ω=EN with an a priori measure p on the state space E. Given a potential f:Ω→R one can ask: among the invariant probabilities which one is the equilibrium probability μ for the interaction described by f? As usual the equilibrium probability for f is the one maximizing pressure. We will present here the case of the product type potential on the one-dimensional lattice system and in this setting we can show the explicit expression of the equilibrium probability. We will also consider questions about Ergodic Optimization, maximizing probabilities, subactions and we will show selection of a maximizing probability, when temperature goes to zero. Finally we show a large deviation principle when temperature goes to zero and we present an explicit expression for the deviation function.

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