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Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules.

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This study demonstrates that certain two-dimensional bootstrap percolation models exhibit a sharp metastability transition. This finding applies to models with isotropic threshold rules and convex symmetric neighborhoods, generalizing previous results.

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Area of Science:

  • Statistical Physics
  • Probability Theory
  • Mathematical Physics

Background:

  • Bootstrap percolation models are fundamental in studying phase transitions.
  • Previous research focused on specific rules, limiting generalizability.
  • Understanding metastability is crucial for complex systems.

Purpose of the Study:

  • To establish a sharp metastability transition for a broader class of 2D bootstrap percolation models.
  • To generalize findings beyond specific, previously studied rules.
  • To provide a contemporary perspective on bootstrap percolation theory.

Main Methods:

  • Analysis of two-dimensional critical bootstrap percolation models.
  • Focus on isotropic threshold rules with convex symmetric neighborhoods.
  • Mathematical proofs establishing the transition.

Main Results:

  • A class of bootstrap percolation models exhibits a sharp metastability transition.
  • This includes all isotropic threshold rules with convex symmetric neighborhoods.
  • The findings extend prior results for specific percolation rules.

Conclusions:

  • The identified class of models demonstrates universal metastability behavior.
  • This work unifies and extends previous specific findings.
  • The study offers a modern framework for bootstrap percolation universality.