Related papers: The Curie-Weiss model -- an approach using moments
The synthesis of molecular magnets has undergone rapid progress in recent years. Each of the identical molecular units can contain as few as two and up to several dozens of paramagnetic ions (spins). Although these materials appear as…
We study the problem of reconstructing the probability measure of the Curie-Weiss model from a sample of the voting behaviour of a subset of the population. While originally used to study phase transitions in statistical mechanics, the…
We study the metastable minima of the Curie-Weiss Potts model with three states, as a function of the inverse temperature, and for arbitrary vector-valued external fields. Extending the classic work of Ellis/Wang and Wang we use singularity…
The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
We use Rice's formulas in order to compute the moments of some level functionals which are linked to problems in oceanography and optics. For instance, we consider the number of specular points in one or two dimensions, the number of…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a "meta-stable set." In the example of the…
This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…
The paper firstly argues from conservation principles that, when dealing with physics aside from elementary particle interactions, the number of naturally independent quantities, and hence the minimum number of base quantities within a unit…
We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.
Let $\{X_n\}_{n\geq 1}$ be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centered sequence with a suitable level of negative dependence. We prove Baum-Katz type theorems by only assuming that the…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
Computationalism provides a framework for understanding how a mathematically describable physical world could give rise to conscious observations without the need for dualism. A criterion is proposed for the implementation of computations…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
We consider a class of self-similar, continuous Gaussian processes that do not necessarily have stationary increments. We prove a version of the Breuer-Major theorem for this class, that is, subject to conditions on the covariance function,…
The anisotropic quantum Heisenberg model with Curie-Weiss-type interactions is studied analytically in several variants of the microcanonical ensemble. (Non)equivalence of microcanonical and canonical ensembles is investigated by studying…
In the mid-19th century, both the laws of mechanics and thermodynamics were known, and both appeared fundamental. This was changed by Boltzmann and Gibbs, who showed that thermodynamics can be *derived*, by applying mechanics to very large…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…