Related papers: Introduction to (generalized) Gibbs measures
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
This lecture will present a review of the past and present tests of the General Relativity theory. The essentials of the theory will be recalled and the measurable effects will be listed and analyzed. The main historical confirmations of…
With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings,…
The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$. We…
A common goal in statistics and machine learning is estimation of unknowns. Point estimates alone are of little value without an accompanying measure of uncertainty, but traditional uncertainty quantification methods, such as confidence…
We consider the system of particles on a finite interval with pair-wise nearest neighbours interaction and external force. This model was introduced by Malyshev to study the flow of charged particles on a rigorous mathematical level. It is…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all…
An introduction into the fundamental quests addressed in space missions is given. These quests are the exploration of the relativistic gravitational field, the Universality of Free Fall, the Universality of the Gravitational Redshift, Local…
Lecture notes as per the title. In the first part, the concepts of a measurable space, measurable maps between measurable spaces and that of a measure on a measurable space are introduced, after which the fundamentals of the theory of…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric,…
The use of the loudest observed event to generate statistical statements about rate and strength has become standard in searches for gravitational waves from compact binaries and pulsars. The Bayesian formulation of the method is…
We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction…