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Lecture Notes on Free Probability
This note contains below topics, Noncommutative probability spaces and distributions, Free Cumulants, Additive free convolution and limit theorems, Asymptotic Freeness, Stransform, Subordination, Operatorvalued noncommutative random variables, Rdiagonal variables, Distributions of SelfAdjoint Variables and Their Transforms, Scaling Properties.
Author(s): Vladislav Kargin
148 Pages 
Lecture Notes on Free Probability Theory
to free probability theory, covering the basic combinatorial and analytic theory, as well as the relations to random matrices and operator algebras. This note contains below topics, Very Short Introduction into Subject and History, The Notion of Freeness Definition Example and Basic Properties, Emergence of the Combinatorics of Free Probability Theory Free Central Limit Theorem, The Combinatorics of Free Probability Theory Free Cumulants, Free Convolution of Compactly Supported Probability Measures and the RTransform, Free Convolution of Arbitrary Probability Measures and the Subordination Function, Gaussian Random Matrices and Asymptotic Freeness, Unitary Random Matrices and Asymptotic Freeness and a Remark on Wigner Matrices, Von Neumann Algebras The Free Group Factors and Relation to Freeness, Circular and RDiagonal Operators, Applications of Freeness to von Neumann Algebras Compression of Free Group Factors, Some More Operator Algebraic Applications of Free Probability.
Author(s): Roland Speicher
119 Pages
Generalized Probability Theory notes for a short course
These notes treat quantum theory as a nonclassical probability calculus. They come from a short course on generalized probability theories. The idea goes back to von Neumann and to the later literature on quantum logics.
Author(s): Alex Wilce
75 Pages
Probability Theory and Examples
This note covers measure theory, Laws of large numbers, Central limit theorem, Martingales, Markov chains, Ergodic theorems, Brownian motion, Applications to random walk, Multidimensional Brownian motion.
Author(s): Rick Durrett
490 Pages
This note explains the following topics, events and probabilities, Combining events, Conditional probabilities, independence and bayes rule, Random variables and discrete distributions, Expectation and variance, Continuous random variables.
Author(s): Sharon Goldwater, University of Edinburgh
34 Pages
Probability Theory Lecture Notes by Phanuel Mariano
The contents include, Combinatorics, Axioms of Probability, Independence, Conditional Probability and Independence, Random Variables, Some Discrete Distributions, Continuous Random Variable, Normal Distributions, Normal approximations to the binomial, Some continuous distributions, Multivariate distributions, Expectations, Moment generating functions, Limit Laws.
Author(s): Phanuel Mariano
98 Pages
Lecture Notes Probability Theory
This book explains the following topics, Probability spaces, Random variables, Independence, Expectation, Convergence of sequences of random variables.
Author(s): Manuel Cabral Morais
275 Pages
These notes are intended to give a solid introduction to Probability Theory with a reasonable level of mathematical rigor. Topics covered includes, Elementary probability, Discretetime finite state Markov chains, Existence of Markov Chains, Discretetime Markov chains with countable state space, Probability triples, Limit Theorems for stochastic sequences, Moment Generating Function, The Central Limit Theorem, Measure Theory and Applications.
Author(s): Christopher King
124 Pages
Probability and Stochastic Processes
This book covers the following topics, Basic Concepts of Probability Theory, Random Variables, Multiple Random Variables, Vector Random Variables, Sums of Random Variables and LongTerm Averages, Random Processes, Analysis and Processing of Random Signals, Markov Chains, Introduction to Queueing Theory and Elements of a Queueing System.
Author(s): Dongyu Qiu
NA Pages