(1) 7월 24일(금, 오후 3:30 - 5:30)
(2) 7월 27일(월, 오전 10:00-12:00)
(3) 7월 28일(화, 오전 10:00-12:00)
Quantum probability (non-commutative probability) provides a framework for extending the measure-theoretical (Kolmogorovian) probability theory.
The idea traces back to von Neumann (1932), who, aiming at the mathematical foundation for the statistical questions in quantum mechanics, initiated a parallel theory by making a selfadjoint operator and a trace play the roles of a random variable and a probability measure, respectively.
Since around 1980 quantum probability has developed considerably spreading effects on various fields of mathematics and quantum physics.
As one of the recently developed applications, we focus on the asymptotic spectral analysis of growing graphs.
These lectures are based mostly on ``Quantum Probability and Spectral Analysis of Graphs," by A. Hora and N. Obata (Springer, 2007).
1. Basic concepts of quantum probability
2. Growing graphs and spectra
3. Quantum decomposition and Interacting Fock spaces
4. Stieltjes transform and continued fractions
5. From Kesten distribution to the semicircle law
6. Notion of independence and central limit theorems