标题： 图组合方法在马尔可夫链大偏差中的应用 显示英文标题

标题： Graph-combinatorial approach for large deviations of Markov chains

摘要： 我们考虑离散时间马尔可夫链，并研究对偶经验占据测度的大偏差，这对计算纯加性和跳跃型可观测量的波动是有用的。 我们提供了一个有限时间矩生成函数的精确表达式，该表达式通过图组合方法分解为循环和路径贡献，并得到对偶经验占据测度的标度累积生成函数。 所得表达式使我们能够对相互作用项和熵项以及拉格朗日乘数给出物理解释，并可能作为次主导渐近行为的起点。 我们通过一个简单的两状态马尔可夫链来说明该方法的使用。 显示英文摘要

摘要： We consider discrete-time Markov chains and study large deviations of the pair empirical occupation measure, which is useful to compute fluctuations of pure-additive and jump-type observables. We provide an exact expression for the finite-time moment generating function, which is split in cycles and paths contributions, and scaled cumulant generating function of the pair empirical occupation measure via a graph-combinatorial approach. The expression obtained allows us to give a physical interpretation of interaction and entropic terms, and of the Lagrange multipliers, and may serve as a starting point for sub-leading asymptotics. We illustrate the use of the method for a simple two-state Markov chain.