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In this work, we prove the well-posedness and propagation of chaos for a stochastic particle system in mean-field interaction under the assumption that the interacting kernel belongs to a suitable $L_t^q-L_x^p$ space. Contrary to the large…
The smallest deformation of the minimal model M(2,3) that can accommodate Cardy's derivation of the percolation crossing probability is presented. It is shown that this leads to a consistent logarithmic conformal field theory at c=0. A…
We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory…
In arXiv:2212.14023 a decomposition of Gaussian measures on finite-dimensional spaces was introduced, which turned out to be a central technical tool to improve currently known bounds on a long standing conjecture in statistical mechanics…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials over a finite field. The…
We study real left-invariant spin Gaussian fields on $SO(3)$, a special class of non-isotropic random fields used to model the polarization of the Cosmic Microwave Background. Leveraging recent results from "New chaos decomposition of…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated…
The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…
We consider a sub-critical Gaussian multiplicative chaos (GMC) measure defined on the unit interval [0,1] and prove an exact formula for the fractional moments of the total mass of this measure. Our formula includes the case where…
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…
In this article we systematically study the general properties and the single-point moments of the inverse of the Gaussian multiplicative chaos.
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
The affine Gaussian derivative model can in several respects be regarded as a canonical model for receptive fields over a spatial image domain: (i) it can be derived by necessity from scale-space axioms that reflect structural properties of…
We study multivariate trigonometric polynomials, satisfying a set of constraints close to the known Strung-Fix conditions. Based on the polyphase representation of these polynomials relative to a general dilation matrix, we develop a simple…
We review and present some known results for non-linear functionals of Gaussian variables in the context of discrete Gaussian fields defined on the $d$ dimensional lattice. Our main result is a Central Limit Theorem in the spirit of the…
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this goal, the paper develops new geometric and analytical…
In this article we study the decoupling structure and multipoint moment of the inverse of the Gaussian multiplicative chaos. It is also the second part of preliminary work for extending the work in "Random conformal weldings" (by K. Astala,…