We derive a large deviation principle for the density profile of occupation times of random interlacements at a fixed level in a large box of Z, d ≥ 3. As an application, we analyze the asymptotic behavior of the probability that atypically high values of the density profile insulate a macroscopic body in a large box. As a step in this program, we obtain a similar large deviation principle for ...

Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) ho...

Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) ho...

In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures 1 n Pn i=1 δ(Xn i ,X n σn(i) ) where σn is a random permutation and ((X i )1≤i≤n)n≥1 is a triangular array of random variables with suitable properties. As an application we show how this result allows to improve the Large Deviation Principles for symmetrised initial-terminal conditions bridge ...

We prove joint large deviation principle for the empirical pair measure and empirical locality measure of the near intermediate coloured random geometric graph models on n points picked uniformly in a d-dimensional torus of a unit circumference. From this result we obtain large deviation principles for the number of edges per vertex, the degree distribution and the proportion of isolated vertic...

This paper is devoted to the problem of sample path large deviations for multidimensional queueing models with feedback. We derive a new version of the contraction principle where the continuous map is not well-defined on the whole space: we give conditions under which it allows to identify the rate function. We illustrate our technique by deriving a large deviation principle for a class of net...

An influential theory of increasing returns has been proposed by the economist W. B. Arthur in '80s to explain lock-in phenomenon between two competing commercial products. In most simplified situation there are products that gain customers according a majority mechanism: each new customer arrives and asks which product they bought certain odd number previous customers, then buy shared within t...