Sample path large deviations for a class ofMarkov chains related to disordered mean field models
- Bovier, Anton
- Gayrard, Véronique
2010 Mathematics Subject Classification
- 60F10 82C44 60J10
- Large deviations, stochastic dynamics, Markov chains, disordered Large deviations, disordered systems, mean field models
We prove a large deviation principle on path space for a class of discrete time Markov processes whose state space is the intersection of a regular domain Λ ⊂ ℝd with some lattice of spacing ∈. Transitions from x to y are allowed if ∈-1(x-y) ∈ Δ for some fixed set of vectors Δ. The transition probabilities p∈(t,x,y), which themselves depend on ∈, are allowed to depend on the starting point x and the time t in a sufficiently regular way, except near the boundaries, where some singular behaviour is allowed. The rate function is identified as an action functional which is given as the integral of a Lagrange function. Markov processes of this type arise in the study of mean field dynamics of disordered mean field models.