典型SK初始态的拉伸指数混合障碍
Stretched-exponential barriers for typical SK initial states
OpenAI 数学仓库收录的研究手稿。展开查看英文摘要，或标记后让我进一步解释。
具体内容
稿件研究零场Sherrington–Kirkpatrick模型在固定逆温度β>1下、从典型平衡构型出发的混合行为。作者声称证明拉伸指数型障碍：在时间 exp(n^{1/10000}) 时与平衡的总变差距离超过1/4的态，其Gibbs质量在无序上依概率趋于1；结论适用于每格点速率为1的热浴动力学及相同次数的离散更新尝试。摘要未说明证明方法。
- 固定β>1，从典型平衡构型出发存在拉伸指数混合障碍。
- 时间 exp(n^{1/10000}) 时偏离平衡超过1/4的态Gibbs质量趋于1。
- 结论适用于每格点速率1的热浴动力学与离散更新。
AI 产生的研究手稿；收录不表示已完成独立审查或同行评议。
英文原始摘要
At every fixed inverse temperature β > 1, we prove a stretched-exponential obstruction to mixing for the zero-field Sherrington–Kirkpatrick model from typical equilibrium configurations held fixed as initial states. The Gibbs mass of states whose total-variation distance from equilibrium at time $`\exp(n^{1/10000})`$ exceeds 1/4 tends to one in probability over the disorder. This holds for rate-one-per-site heat-bath dynamics and after the same stated number of discrete update attempts.
用户标记：未标记
固定编号：639e09c1a890e668
原文来源