# 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…

## 3 Citations

Microcanonical conditioning of Markov processes on time-additive observables

- MathematicsJournal of Statistical Mechanics: Theory and Experiment
- 2022

The recent study by De Bruyne et al (2021 J. Stat. Mech. 123204), concerning the conditioning of the Brownian motion and of random walks on global dynamical constraints over a finite time-window T,…

Anomalous dynamical large deviations of local empirical densities and activities in the pure and in the random kinetically constrained East model

- PhysicsThe European Physical Journal B
- 2022

The East model is the simplest one-dimensional kinetically-constrained model of N spins with a trivial equilibrium that displays anomalously large spatio-temporal fluctuations, with characteristic…

Linear Response Theory and Fluctuation Dissipation Theorem for Systems with Absorbing States

- Physics
- 2022

The Fluctuation Dissipation Theorem (FDT) is one of the fundamental results of statistical mechanics and is a powerful tool that connects the macroscopic properties to microscopic dynamics. The FDT…

## References

SHOWING 1-10 OF 176 REFERENCES

Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets

- Mathematics
- 2020

Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at…

Quasi-stationary distributions for stochastic processes with an absorbing state

- Mathematics
- 2002

We study the long-time behaviour of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical…

Large deviations for dynamical fluctuations of open Markov processes, with application to random cascades on trees

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

The large deviations at ‘Level 2.5 in time’ for time-dependent ensemble-empirical-observables, introduced by Maes et al (2008 Markov Proc. Relat. Fields 14 445) for the case of independent Markov…

Revisiting the Ruelle thermodynamic formalism for Markov trajectories with application to the glassy phase of random trap models

- Mathematics
- 2021

The Ruelle thermodynamic formalism for dynamical trajectories over the large time T corresponds to the large deviation theory for the information per unit time of the trajectories probabilities. The…

Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates

- Mathematics
- 2021

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady states when the two velocities and/or the two switching rates are space-dependent. A long dynamical…

Nonequilibrium Markov Processes Conditioned on Large Deviations

- Mathematics
- 2015

We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic…

Quasi-stationary distributions and population processes

- Mathematics
- 2012

This survey concerns the study of quasi-stationary distributions with
a specific focus on models derived from ecology and population
dynamics. We are concerned with the long time behavior of…

Metastability and Low Lying Spectra¶in Reversible Markov Chains

- Mathematics
- 2000

Abstract: We study a large class of reversible Markov chains with discrete state space and transition matrix PN. We define the notion of a set of metastable points as a subset of the state space ΓN…