Consider the inhomogeneous Erd\H{o}s-R\'enyi random graph (ERRG) on $n$ vertices for which each pair $i,j\in\{1,\ldots,n\}$, $i\neq j$ is connected independently by an edge with probability $r_n(\frac{i-1}{n},\frac{j-1}{n})$, where $(r_n)_{n\in\mathbb{N}}$ a sequence of graphons converging to reference graphon $r$. As generalization celebrated LDP ERRGs Chatterjee and Varadhan (2010), Dhara Sen...

For a powered Poisson process, we define Signal-to-Interference-plus-Noise Ratio(SINR) and thesinr network as Telecommunication Network. We the Empirical Measures (empirical measure, empirical link measure sinr measure) of class Networks. this Network prove joint large deviation principle(LDP) for measures All our rate functions are expressed in terms relative entropies.

This work is concerned with a Freidlin--Wentzell type large deviation principle for family of multiscale quasilinear and semilinear stochastic partial differential equations. Employing the weak c...

We prove a large deviation principle for the finite dimensional marginals of the Gibbs distribution of the macroscopic ‘overlap’-parameters in the Hopfield model in the case where the number of random ‘patterns’, M , as a function of the system size N satisfies lim supM(N)/N = 0. In this case the rate function is independent of the disorder for almost all realizations of the patterns.

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the scaled Yang-Mills measures satisfy a large deviation principle with the Yang-Mills energy as rate function. This gives some rigorous content to the informal description of the Yang-Mills measure as the Gibbs measure of the Yang-Mills...

We derive a large deviation principle for a Brownian immigration branching particle system, where the immigration is governed by a Poisson randommeasurewith a Lebesgue intensity measure.