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This chapter uses the setting of the FA-2f model to develop several new tools for determining the emptying time of the origin with high precision as \(q\rightarrow 0\) . We begin by using bisection in higher dimensions to show that this time scale is finite. We then discuss a robust long range Poincaré inequality approach for proving upper bounds. Finally, we assess the sharp threshold of FA-2f, which relies on a robust relation with bootstrap percolation for the lower bound and on the very flexible method of matryoshka dolls for the upper bound. All of these methods generalise to treat various other models.

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Fredrickson-Andersen 2-Spin Facilitated Model

  • 章节

  • 发表日期：

    2025年

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  • Ivailo Hartarsky,
  • Cristina Toninelli

摘要

This chapter uses the setting of the FA-2f model to develop several new tools for determining the emptying time of the origin with high precision as \(q\rightarrow 0\) . We begin by using bisection in higher dimensions to show that this time scale is finite. We then discuss a robust long range Poincaré inequality approach for proving upper bounds. Finally, we assess the sharp threshold of FA-2f, which relies on a robust relation with bootstrap percolation for the lower bound and on the very flexible method of matryoshka dolls for the upper bound. All of these methods generalise to treat various other models.