Sample path large deviations for a class of Markov chains related to disordered mean field models

الأصل · EN

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 Ł⊂ ᵈ with some lattice of spacing. Transitions from x to y are allowed if ⁻¹(x-y)∈ for some fixed set of vectors. 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. %of time dependent relativistic classical mechanics. Markov processes of this type arise in the study of mean field dynamics of disordered mean field models.