For the sum of squares of an autoregressive system, the large deviation principle with the explicit rate function is established. AMS 1991 Subject Classification: Primary 60FlO.

For a $d-$regular random model, we assign to vertices $q-$state spins. From this model, we define the \emph{empirical co-operate measure}, which enumerates the number of co-operation between a given couple of spins, and \emph{ empirical spin measure}, which enumerates the number of sites having a given spin on the $d-$regular random graph model. For these empirical measures we obtain large devi...

For any hyperbolic rational map and any net of Borel probability measures on the space of Borel probability measures on the Julia set, we show that this net satisfies a strong form of the large deviation principle with a rate function given by the entropy map if and only if the large deviation and the pressure functionals coincide. To each such principles corresponds a new expression for the en...

In this paper, we analyze a scheduling algorithm which is suitable for the heterogeneous traffic network. In the large deviation setting, we are interested to see, how the asymptotic decay rate of maximum queue overflow probability achieved by this algorithm.We first derive an upper bound on the decay rate of the queue overflow probability as the queue overflow threshold approaches infinity. Th...

A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost surely. This includes all the known cases as well as some heavy-tailed distributions. 1. Introduction. The purpose of this note is to bring out the essence in...

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

Abstract. For any finite coloured graph we define the empirical neighbourhood measure, which counts the number of vertices of a given colour connected to a given number of vertices of each colour, and the empirical pair measure, which counts the number of edges connecting each pair of colours. For a class of models of sparse coloured random graphs, we prove large deviation principles for these ...

Abstract. For a finite typed graph on n nodes and with type law μ, we define the socalled spectral potential ρλ( ·, μ), of the graph.From the ρλ( ·, μ) we obtain Kullback action or the deviation function, Hλ(π ‖ ν), with respect to an empirical pair measure, π, as the Legendre dual. For the finite typed random graph conditioned to have an empirical link measure π and empirical type measure μ, w...

Abstract. In this article we prove a local large deviation principle (LLDP) for the critical multitype Galton-Watson process from spectral potential point. We define the so-called a spectral potential UK( ·, π) for the Galton-Watson process, where π is the normalized eigen vector corresponding to the leading Perron-Frobenius eigen value 1l of the transition matrix A(·, ·) defined from K, the tr...