Related papers: Introduction to (generalized) Gibbs measures
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
In statistical learning theory, a generalization bound usually involves a complexity measure imposed by the considered theoretical framework. This limits the scope of such bounds, as other forms of capacity measures or regularizations are…
We introduce a generalization of the cavity, or Bethe-Peierls, method that allows to follow Gibbs states when an external parameter, e.g. the temperature, is adiabatically changed. This allows to obtain new quantitative results on the…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
A novel measure, quantumness of correlations is introduced here for bipartite states, by incorporating the required measurement scheme crucial in defining any such quantity. Quantumness coincides with the previously proposed measures in…
Given a finite-to-one map acting on a compact metric space, one classically constructs for each potential in an appropriate Banach space of functionsa transfer operator acting on functions. Under suitable condition, the…
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…
The present review is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich). Being bounded by lecture frames, the selection of the material, by…
The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to…
Gibbs partition models are the largest class of infinite exchangeable partitions of the positive integers generalizing the product form of the probability function of the two-parameter Poisson-Dirichlet family. Recently those models have…
We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…
The paper gives a bound on the generalization error of the Gibbs algorithm, which recovers known data-independent bounds for the high temperature range and extends to the low-temperature range, where generalization depends critically on the…
Motivated by the growing interest on PT-quantum mechanics, in this paper we discuss some facts on generalized Gibbs states and on their related KMS-like conditions. To achieve this, we first consider some useful connections between similar…
The statistics of particles and extended excitations, such as loops and membranes, are fundamental to modern condensed matter physics, high-energy physics, and quantum information science, yet a comprehensive lattice-level framework for…
In this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a Gibbs…
These notes are an outgrowth of an advanced undergraduate course taught at the University of Maryland, College Park. They are intended as an introduction to various aspects of particle and nuclear physics with an emphasis on the role of…
The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed form. In this case, sensitivity is…
Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many…
These are notes based on lectures given at the 2021 summer school on Fundamental Problems in Statistical Physics XV. Their purpose is to give a very brief introduction to Generalized Hydrodynamics, which provides a description of the large…
This article contains the lecture notes for the short course ``Introduction to Econophysics,'' delivered at the II Brazilian School on Statistical Mechanics, held in Sao Carlos, Brazil, in February 2004. The main goal of the present notes…