Related papers: Gibbs and Quantum Discrete Spaces
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We…
We present a general method to derive continuity estimates for conditional probabilities of general (possibly continuous) spin models sub jected to local transformations. Such systems arise in the study of a stochastic time-evolution of…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
We suggest commutation relations for a quantum measure. In one version of these relations, the right-hand side takes account of the presence of curvature of space; in the simplest case, this yields the action of general relativity. We…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
A continuous bundle of $C^*$-algebras provides a rigorous framework to study the thermodynamic limit of quantum theories. If the bundle admits the additional structure of a strict deformation quantization (in the sense of Rieffel) one is…
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 model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…