Derivation of the Onsager principle from large deviation theory

Large deviation principle in logarithmic potential theory

Large Deviation Theory

If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a lo...

A large deviation principle for Dirichlet posteriors

Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space Ω, and consider the problem of estimating the law of X1 in a Bayesian framework. A conjugate family of priors for non-parametric Bayesian inference is the Dirichlet process priors popularized by Ferguson. We prove that if the prior distribution is Dirichlet, then the sequence...

Large deviation principle for enhanced Gaussian processes

We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N . We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian motion, in Hölderor modulus topology, appears as special case. © 2007 Elsevier Masson SAS. All rights reserved. Résumé Nous etudions les princ...

A large deviation principle with queueing applications

In this paper, we present a large deviation principle for partial sums processes indexed by the half line, which is particularly suited to queueing applications. The large deviation principle is established in a topology that is finer than the topology of uniform convergence on compacts and in which the queueing map is continuous. Consequently, a large deviation principle for steady-state queue...