Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Probability and Randomness: Quantum versus Classical rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level.
Contents:
Foundations of Probability
RandomnessSupplementary
Notes on Measure-theoretic and Frequency Approaches
Introduction to Quantum Formalism
Quantum and Contextual Probability
Interpretations of Quantum Mechanics and Probability
Randomness: Quantum Versus Classical
Probabilistic Structure of Bell''s Argument
Quantum Probability Outside of Physics: from Molecular Biology to Cognition