# Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

@article{Monthus2022LargeDF, title={Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment}, author={C. Monthus}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2022}, volume={2022} }

The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood…

## 5 Citations

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