Related papers: Large deviation principles for hypersingular Riesz…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle operators with law given through the…
We study microscopic observables of the Discrete Gaussian model (i.e., the Gaussian free field restricted to take integer values) at high temperature using the renormalisation group method. In particular, we show the central limit theorem…
The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by $\beta^*$. In this paper we generalize a…
We prove limit theorems for rescaled occupation time fluctuations of a (d,alpha,beta)-branching particle system (particles moving in R^d according to a spherically symmetric alpha-stable Levy process, (1+beta)-branching, 0<beta<1, uniform…
We derive the large-N, all order asymptotic expansion for a system of N particles with mean-field interactions on top of a Coulomb repulsion at temperature 1/\beta, under the assumptions that the interactions are analytic, off-critical, and…
A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become…
In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
We establish precise upper-tail asymptotics and large deviation principles for the rightmost eigenvalue $\lambda_1$ of Wigner matrices with sub-Gaussian entries. In contrast to the case of heavier tails, where deviations of $\lambda_1$ are…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
Let L be a positive line bundle over a projective complex manifold X. Consider the space of holomorphic sections of the tensor power of order p of L. The determinant of a basis of this space, together with some given probability measure on…
We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The…
We consider a non-uniquely ergodic dynamical system given by a $\mathbb{Z}^{l}$-action (or $(\N\cup\{0\})^l$-action) $\tau$ on a non-empty compact metrisable space $\Omega$, for some $l\in\N$. Let (D) denote the following property: The…
We derive the complete asymptotic expansion in terms of powers of $N$ for the Riesz $s$-energy of $N$ equally spaced points on the unit circle as $N\to \infty$. For $s\ge -2$, such points form optimal energy $N$-point configurations with…
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…
In this work we determine a process-level Large Deviation Principle (LDP) for a model of interacting particles indexed by a lattice $\mathbb{Z}^d$. The connections are random, sparse and unscaled, so that the system converges in the large…
We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…
We study the long-range one-dimensional Riesz gas on the circle, a continuous system of particles interacting through a Riesz kernel. We establish near-optimal rigidity estimates on gaps valid at any scale. Leveraging these local laws…
We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we…