Chandra Nair - Theory of Probability

IERG 6300 Theory of Probability

Course Information

Course Outline (planned)

  • Measure-theoretic foundations of probability theory
  • Characteristic functions and Weak Convergence
  • Independent Sums - Limit theorems and Concentration Inequalities
  • Dependent random variables - Conditional Expectation and Markov Chains
  • Martingales: convergence theorems and inequalities
  • Elements of ergodic theory (time-permitting)
  • Course Material

    Remarks : The framework of the class as well as the initial material follow Probability Theory (Courant Lecture Notes) by S.R.S. Varadhan I have also borrowed some material and exercises from Prof. Amir Dembo's notes that he had shared with me. Towards the latter part, there are results that have been borrowed from other references as well. I would urge students who like references to look at the list in Prof. David Aldous's course webpage.

    The aim of this class is to build a minimal set of tools and ideas that are needed to prove certain central results in this area.

    The lecture notes below are essentially from scribed notes by students from previous years' offerings. The arguments in the notes are bound to have transcribing errors as well as certain sections that need additional work (that was done on the board) to turn it into a complete argument. Therefore, please use these notes with caution.