记录时间与积分电流精度的精确渐近等价性
Exact asymptotic equivalence between precisions of record-times and integrated currents
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中文总结 AI 辅助
本文证明连续时间马尔可夫跳变过程中积分电流的Fano因子与记录间等待时间平方变异系数精确相等，通过更新结构与Narayana数统一了电流涨落的描述，并将结果推广至任意有限状态图。
中文摘要 AI 辅助
我们建立了连续时间马尔可夫跳跃过程中积分电流的涨落与电流记录事件的时间统计之间的精确等价关系。具体而言，我们证明，在最小假设下，积分电流的Fano因子与记录间等待时间的平方变异系数精确一致。这一结果是通过证明记录间时间诱导出更新结构而获得的，因为每个记录事件都将系统重置到一个固定状态，并且其生成函数可以精确地用由Narayana数支配的组合组织来表示。该等价性将先前针对单环网络获得的结果推广到任意有限状态图，并为电流涨落提供了基于记录时间可观测量的统一表示。这些结果在纯概率框架内推导，并阐明了电流精度的结构起源，即其与首次通过类事件统计的关系。
英文摘要
We establish an exact equivalence between the fluctuations of integrated currents and the temporal statistics of current record events in continuous-time Markov jump processes. Specifically, we show that, under minimal assumptions, the Fano factor of an integrated current coincides exactly with the squared coefficient of variation of the inter-record waiting times. This result is obtained by showing that inter-record times induce a renewal structure, since each record event resets the system to a fixed state, and that their generating function can be expressed exactly in terms of a combinatorial organization governed by Narayana numbers. The equivalence extends previous results obtained for unicyclic networks to arbitrary finite-state graphs and provides a unified representation of current fluctuations in terms of record-time observables. The results are derived within a purely probabilistic framework and clarify the structural origin of current precision in terms of first-passage-like event statistics.
发表机构
- University of Padova（帕多瓦大学）
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