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Probability: Theory and Examples
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In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.Abstract:
This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems.read more
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A Probabilistic Theory of Pattern Recognition
TL;DR: The Bayes Error and Vapnik-Chervonenkis theory are applied as guide for empirical classifier selection on the basis of explicit specification and explicit enforcement of the maximum likelihood principle.
Book ChapterDOI
An Introduction to Ergodic Theory
TL;DR: Ergodic theory concerns with the study of the long-time behavior of a dynamical system as mentioned in this paper, and it is known as Birkhoff's ergodic theorem, which states that the time average exists and is equal to the space average.
Book ChapterDOI
Introduction to the non-asymptotic analysis of random matrices.
TL;DR: This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory, particularly for the problem of estimating covariance matrices in statistics and for validating probabilistic constructions of measurementMatrices in compressed sensing.
Proceedings ArticleDOI
Spray and wait: an efficient routing scheme for intermittently connected mobile networks
TL;DR: A new routing scheme, called Spray and Wait, that "sprays" a number of copies into the network, and then "waits" till one of these nodes meets the destination, which outperforms all existing schemes with respect to both average message delivery delay and number of transmissions per message delivered.
Book
Network Information Theory
Abbas El Gamal,Young-Han Kim +1 more
TL;DR: In this article, a comprehensive treatment of network information theory and its applications is provided, which provides the first unified coverage of both classical and recent results, including successive cancellation and superposition coding, MIMO wireless communication, network coding and cooperative relaying.
References
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Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI