Related papers: Gibbs measures based on 1D (an)harmonic oscillator…
For a wide class of domains $G\subset\mathbb C^d$ including balls and polydisks we prove the density of their canonical image in the spectrum of $H^\infty(G)$. This Corona Theorem is proved first in its abstract version for certain uniform…
We study Gibbs measures with log-correlated base Gaussian fields on the $d$-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson's argument. In this paper, we consider the focusing case with…
In this note we study a class of specifications over $d$-dimensional Wiener measure which are invariant under uniform translation of the paths. This degeneracy is removed by restricting the measure to the $\sigma$-algebra generated by the…
We consider a class of non-conformal expanding maps on the $d$-dimensional torus. For an equilibrium measure of an H\"older potential, we prove an analogue of the Central Limit Theorem for the fluctuations of the logarithm of the measure of…
Positive operator measures (with values in the space of bounded operators on a Hilbert space) and their generalizations, mainly positive sesquilinear form measures, are considered with the aim of providing a framework for their generalized…
We prove the validity of a small noise large deviation principle for the family of invariant measures $\{\mu_\epsilon\}_{\epsilon>0} $ associated to the one dimensional stochastic Allen-Cahn equation with inhomogeneous Dirichlet boundary…
We study the finite dimensional marginals of the Gibbs measure in the Hopfield model at low temperature when the number of patterns, $M$, is proportional to the volume with a sufficiently small proportionality constant $\a>0$. It is shown…
We consider the local dimension spectrum of a weak Gibbs measure on a C^1 non-uniformly hyperbolic system of Manneville- Pomeau type. We present the spectrum in three ways: using invariant measures, uniformly hyperbolic ergodic measures and…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given.…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…
The efficient readout of the relevant information is pivotal for quantum simulation experiments. Often only single observables are accessed by performing standard projective measurements. In this work, we implement a generalized measurement…
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of "symmetric measure": exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts…
We prove that, for a $C^2$ partially hyperbolic endomorphism of the 2-torus which is strongly transitive, given an ergodic $u$-Gibbs measure that has positive center Lyapunov exponent and has full support, then either the map is special…
We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…
We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under…
We prove that a partially hyperbolic attracting set for a C2 vector field, having slow recurrence to equilibria, supports an ergodic physical/SRB measure if, and only if, the trapping region admits non-uniform sectional expansion on a…
We consider the defocusing nonlinear Schr\"odinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the…
We consider some of the main notions of Gibbs measures on subshifts introduced by different communities, such as dynamical systems, probability, operator algebras, and mathematical physics. For potentials with $d$-summable variation, we…
The mean-field approximations of many-boson dynamics are known to be effective in many physical relevant situations. The mathematical justifications of such approximations rely generally on specific considerations which depend too much on…