In this paper systems of functional equations in infinitely many variables arising in combinatorial enumeration problems are studied. We prove sufficient conditions under which the combinatorial random variables encoded in the generating functions of the system tend to an infinite dimensional Gaussian limiting distribution.

We consider an elliptic pseudo-differential equation with a highly oscillating linear potential modeled as a stationary ergodic random field. The random field is a function composed with a centered long-range correlated Gaussian process. In the limiting of vanishing correlation length, the heterogeneous solution converges to a deterministic solution obtained by averaging the random potential. W...

Abstract. It is well known that the ratio of two independent standard Gaussian random variables follows a Cauchy distribution. Any convex combination of independent standard Cauchy random variables also follows a Cauchy distribution. In a recent joint work [PM16], the author proved a surprising multivariate generalization of the above facts. Fix m > 1 and let Σ be a m × m positive semi-definite...

So-called full line concentration graphs represent a set of random variables by the vertices of an undirected graph. That is, some, but in general not all, pairs of vertices are joined by edges and a missing edge between, say, vertices i and j implies that the corresponding random variables are conditionally independent given all remaining variables. If the joint distribution is multivariate Ga...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

We investigate the asymptotic mesoscopic behavior of a spatially extended stochastic neural networks dynamics in random environment with highly random connectivity weights. These systems model the spatiotemporal activity of the brain, thus feature (i) communication delays depending on the distance between cells and (ii) heterogeneous synapses: connectivity coefficients are random variables whos...

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family...

Several proofs of the monotonicity of the nonGaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were published. We give an upper bound on the decrease rate of the non-Gaussianness which is proportional to the inverse of n, for large n. The proof is based on ...

I. INTRODUCTION Boltzmann machines are probability distributions on high dimensional binary vectors which are analogous to Gaussian Markov Random Fields in that they are fully determined by first and second order moments. A key difference however is that augmenting Boltzmann machines with hidden variables enlarges the class of distributions that can be modeled, so that in principle it is possib...