Probability theory

Schramm–Loewner Evolution

Self-study notes following the notes of N. Berestycki & J.R. Norris.

A Conjecture on Linear Combinations of Rademacher Random Variables

A seemingly innocent unsolved problem on the sum of Rademacher random variables (taking values $+ 1$ and $-1$ with equal probability $\frac{1}{2}$).

Notes for the summer school on Random Media at Colorado State Univeristy.

A Random Walk to Stochastic Analysis

Notes and references to study stochastic calculus.

A Rough Path to KPZ

Notes and references on topics that bear KPZ (Kardar-Parisi-Zhang) in the spirit.

What is Free Probability?

Notes on the subject of free probability theory. In a nutshell, working in an abstract setting allows a generalization of classical probability theory.