标题： 图组合方法用于马尔可夫链的大偏差 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，这有助于计算纯加性和跳跃型可观测量的波动。 我们通过图组合方法提供了对偶经验占据测度的有限时间矩生成函数和标度累积生成函数的精确表达式。 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子给出物理解释，并可能作为次主导渐近行为的起点。 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 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.