Requirements: Analysis
Basic concepts for chances. Offered Spring 2018.
Content: Formulation of random variables, Distribution functions, Conditional probability, Multivariate distributions, MGF, Central limit theorems.
Real modeling evolving time. Theoretical, practical and computational! Offered Fall 2018.
Content: Markov chains, Poisson processes, Renewals, CTMC, BM.
https://en.wikipedia.org/wiki/Random_walk
Partial sum of random variables/movements.
Keywords: Recurrence and transience, Asymptotic behavior.
Keywords: Probabilistic analysis of algorithms and stochastic optimizations, Random graphs and networks, Integrable probability (combinatorics).
The bridge between Probabilistic Math and the real world. In late 19th century, theoretical physicists use probability models to discuss the microscopic phenomena. Since then, probability goes to the direction different from statistics.
Keywords: Gibbs free energy, Ising models, Disordered systems, MCMC
Probability theory is based on measure theory since 1930's. Offered Fall 2020.
Indistinguishable is typical in physics.
2019 NCTS Summer Course: Spectrally Negative Levy Processes and Applications
2018 NCTS Summer Course: Random Walks and Related Topics, July 23 - August 2, 2018
NCTS Random Matrices Seminar, Time: September 22, 2017 - February 15, 2018
2017 NCTS Summer Course on Free Probability
2016 NCTS Probability Summer Courses July 25 - August 16, 2016
Topic I: Introduction to Stochastic Calculus and Applications
Topic II: Markov Chains and Mixing Times
2015 NCTS Short Course on Random Walks July 14 - 28, 2015
Regularly Summer Program: Mathematical finance and FinTech