Related papers: Interacting generalized Friedman's urn systems

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…

We present a theory for the low-temperature properties of a resonantly interacting Fermi mixture in a trap, that goes beyond the local-density approximation. The theory corresponds essentially to a Landau-Ginzburg-like approach that…

This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…

We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state.…

It is well known that in a small P\'olya urn, i.e., an urn where second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically…

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…

We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic…

Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…

In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood it is still not very clear what happens to…

Invertible neural networks (INNs) are neural network architectures with invertibility by design. Thanks to their invertibility and the tractability of Jacobian, INNs have various machine learning applications such as probabilistic modeling,…

An urn scheme is a probabilistic model in which balls are placed into urns sequentially and independently of each other. All balls share the same probability distribution for hitting the urns. In the simplest case, there is a finite number…

Generating realistic artificial preference distributions is an important part of any simulation analysis of electoral systems. While this has been discussed in some detail in the context of a single electoral district, many electoral…

We address the issue of the proximity of interacting diffusion models on large graphs with a uniform degree property and a corresponding mean field model, i.e. a model on the complete graph with a suitably renormalized interaction…

Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…

In this paper, we consider a system of heterogeneously interacting quantum particles subject to indirect continuous measurement. The interaction is assumed to be of the mean-field type. We derive a new limiting quantum graphon system, prove…

This paper present the important role that random system with complete connections played in solving the Gauss problem associated to the regular continued fractions. Hence, using the ergodic behavior of homogeneous random system with…

This paper studies a general class of Iterated Function Systems (IFS). No contractivity assumptions are made, other than the existence of some compact attractor. The possibility of escape to infinity is considered. Our present approach is…

In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional statistical mechanics models at the critical point, including:…