This paper discusses the large-deviation principle of discriminant statistics for Gaussian locally stationary processes. First, large-deviation theorems for quadratic forms and the log-likelihood ratio for a Gaussian locally stationary process with a mean function are proved. Their asymptotics are described by the large deviation rate functions. Second, we consider the situations where processe...

We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.

There is an extensive literature on the large deviation principle under various dependence structures. However, in comparison to other limit theorems, few papers deal with strong mixing dependence conditions. In this note we prove the large deviation principle for 4-mixing stationary random sequences with fast enough convergence rate and for $-mixing stationary random sequences. Our d-mixing re...

We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on Zd. We complement the analysis of Zerner (1996), where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting.

We establish functional large deviation principles (FLDPs) for waiting and departure processes in single-server queues with unlimited waiting space and the rst-in rst-out service discipline. We apply the extended contraction principle to show that these processes obey FLDPs in the function space D with one of the non-uniform Skorohod topologies whenever the arrival and service processes obey FL...