Related papers: Ruelle-Lanford functions for quantum spin systems
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
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…
In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these…
Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the…
A basic result of large deviations theory is Sanov's theorem, which states that the sequence of empirical measures of independent and identically distributed samples satisfies the large deviation principle with rate function given by…
In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
We consider translation invariant gapped quantum spin systems satisfying the Lieb-Robinson bound and containing single-particle states in a ground state representation. Following the Haag-Ruelle approach from relativistic quantum field…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
An information theory description of finite systems explicitly evolving in time is presented for classical as well as quantum mechanics. We impose a variational principle on the Shannon entropy at a given time while the constraints are set…
We consider discrete time Markov chains with Polish state space. The large deviations principle for empirical measures of a Markov chain can equivalently be stated in Laplace principle form, which builds on the convex dual pair of relative…
We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs…
Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large deviation principle for Smale spaces, in…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
A family of heterogeneous mean-field systems with jumps is analyzed. These systems are constructed as a Gibbs measure on block graphs. When the total number of particles goes to infinity, a law of large numbers is shown to hold in a…
We present a separable version of Loop Quantum Gravity (LQG) based on an inductive system of cubic lattices. We construct semi-classical states for which the LQG operators -- the flux, the area and the volume operators -- have the right…
We establish large deviation estimates related to the Dynkin--Lamperti theorem, which is a distributional limit theorem for the position of a subordinator immediately before it crosses a fixed level. Our approach relies on the theory of…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
We obtain a first order extension of the large deviation estimates in the G\"{a}rtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order…
Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \infty] $ such that, for all $\alpha \in…