2018/07/17 by Francesco Manzo, Manzo, F., Elisabetta Scoppola +1
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Software System Performance and Reliability
paper · pdf · doi:10.48550/arxiv.1807.11574
openalex publication_date 2018/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set G are obtained. A new notion of "strong metastability time" is introduced to describe the local relaxation time. This time is defined via a generalization of the strong stationary time to a "conditionally strong quasi-stationary time"(CSQST). Rarity of the target set G is not required and the initial distribution can be completely general. The results clarify the the role played by the initial distribution on the exponential law; they are used to give a general notion of metastability and to discuss the relation between the exponential distribution of the first hitting time and metastability.