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Recently methods have been developed which exploit the chiral symmetry of QCD in order to make rigorous contact with low energy particle physics phenomenology. In these lectures we present a pedagogical introduction to these techniques.
In this paper we present the molecular theory of viscosity of confined fluids in small or nano systems. This theory is also applicable to the interfacial viscosity. The basis of this research work is the Enskog kinetic theory and the…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
We investigate the description of current transfer in polycrystalline superconductors by percolation theory and its limitations. Various computer models that have been proposed are reviewed and related to the experimental and theoretical…
To appear to MCMC handbook, S. P. Brooks, A. Gelman, G. Jones and X.-L. Meng (eds), Chapman & Hall.
These expository notes propose to follow, across fields, some aspects of the concept of entropy. Starting from the work of Boltzmann in the kinetic theory of gases, various universes are visited, including Markov processes and their…
Markov chains arising from random iteration of functions $S_{\theta}:X\to X$, $\theta \in \Theta$, where $X$ is a Polish space and $\Theta$ is arbitrary set of indices are considerd. At $x\in X$, $\theta$ is sampled from distribution…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
The present overview of interacting particle systems on random graphs collects the notes of a mini-course given by the authors at the Brazilian School of Probability, 5--9 August 2024, in Salvador, Bahia, Brazil. The content is a personal…
The main input of this note is to provide an alternative probabilistic approach to the ${\Phi}^{2n}$ theory in dimension 2, based on concentration phenomenon of martingales associated to polynomials of Gaussian variables. This is based on…
This is a brief introduction to the statistical theory of fluid turbulence, with an emphasis on the field-theoretic treatment of renormalized viscosity and energy fluxes.
Correction to Annals of Applied Probability 17 (2007) 781--808 [doi:10.1214/105051607000000032].
A mathematical interpretation of the usual definition of entropy (for a discrete probability distribution or a trace 1 positive operator) is given. This formulation makes some properties of entropy immediate.
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
A notion of entangled Markov chain was introduced by Accardi and Fidaleo in the context of quantum random walk. They proved that, in the finite dimensional case, the corresponding states have vanishing entropy density, but they did not…
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied…