Related papers: A functional central limit theorem for a class of …
Quantitative limit theorems for non-linear functionals on the Wiener space are considered. Given the possibly infinite sequence of kernels of the chaos decomposition of such a functional, an estimate for different probability distances…
Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only…
Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…
Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
Using a central limit theorem for arrays of interacting quantum systems, we give analytical expressions for the density of states and the partition function at finite temperature of such a system, which are valid in the limit of infinite…
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…
We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
A functional risk curve gives the probability of an undesirable event as a function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…
A central limit theorem is proved for some strictly stationary sequences of random variables that satisfy certain mixing conditions and are subjected to the "shrinking operators" $U_r(x):=[\max\{|x|-r,0\}]\cdot x/|x|,\ r \ge 0$. For…
Operator self-similar processes, as an extension of self-similar processes, have been studied extensively. In this work, we study limit theorems for functionals of Gaussian vectors. Under some conditions, we determine that the limit of…
In this paper, we introduce a fundamental model for independent and identically distributed sequence with model uncertainty on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels. Thanks…
We develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems. We introduce and study the notion of the Schur generating function of a random discrete configuration. Our main result provides a…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…
A notion of local $U$-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for $U$-processes that may be useful in other contexts. This local…
This paper develops an analytic theory for the study of some Polya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the…