Related papers: Extrapolation and Factorization
Lecture notes given at the summer school ``Applications of random matrices to physics", Les Houches, June 2004.
We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…
We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
Lecture notes for a master-level applied mathematics course on stochastic processes and applications, held at the University of Orl\'eans, France. Contents: Markov chains, Poisson point processes, Markovian jump processes, queueing theory.…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Among many efforts to facilitate timely access to safe and effective medicines to children, increased attention has been given to extrapolation. Loosely, it is the leveraging of conclusions or available data from adults or older age groups…
The fourth edition of the international workshop on Causation, Responsibility and Explanation took place in Prague (Czech Republic) as part of ETAPS 2019. The program consisted in 5 invited speakers and 4 regular papers, whose selection was…
The aim of this expository article is to present recent developments in the centuries old discussion on the interrelations between continuous and differentiable real valued functions of one real variable. The truly new results include,…
These are the unpublished notes on functional analysis, given by Professor Jaime Chica, School of Mathematics, University of Antioquia.
The present overview and gentle introduction to Grassmannian calculus and some of its applications to probability collects the notes of a mini-course given by the authors at the Brazilian School of Probability, August 5-9, 2024, in…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.
Brief lecture notes for a course about random matrices given at the University of Cambridge.
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show…
These are notes based on a course that I gave at the University of Chicago in Fall 2016 on "Loop measures and the loop-erased random walk." This is not intended to be a comprehensive view but rather a personal selection of some key ideas…
The present notes summarise the oligopoly dynamics lectures professor Lu\'is Cabral gave at the Bank of Portugal in September and October 2017. The lectures discuss a set industrial organisation problems in a dynamic environment, namely…
This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda…
This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level…
These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.