Related papers: Free probability for probabilists
Here I discuss ideas that makes a synthesis of topology and probability theory. The idea is the following: given a set $X$, assign a number $p(A)\in [0,1]$ for any subset $A$ of $X$. We can interpret $p(A)$ as the probability of openness of…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. David Freedman and Philip Stark's concept of model based probabilities is examined and is used as a bridge between the formal…
Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to…
In the book we present main concepts of probabilistic automata theory.
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
The paper is an introduction to intuitionistic mathematics.
The issue of defining a random sequence of qubits is studied in the framework of Algorithmic Free Probability Theory.Its connection with Quantum Algorithmic Information Theory is shown
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
In this paper we present three simple applications of probability and highlight and discuss their paradoxical flavour.
A very simple but useful almost sure convergence theorem of probability is given.
We study the analogue of Kummer distribution in free probability. We prove characterization of free-Kummer and free Poisson distributions by freeness properties together with some assumptions about conditional moments. Our main tools are…
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
The concept of freeness was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices. We will show how the combination of various free probability results with a…
An overview of the recent developments in plurifine potential theory.
This article is geared towards theorists interested in estimating parameters of their theoretical models, and computing their own limits using available experimental data and elementary Mathematica code. The examples given can be useful…
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.