# Ma 144B. Probability

### Schedule

MWF 1 pm, Room 122 in Math Building (also known as Building 15)

### About this course

In this course, we explore the basic properties of Brownian motion.
Some topics I hope to cover:

- Brownian motion is locally Holder continuous
- Applications to harmonic functions: recurrence, transience, occupation times
- Conformal invariance and applications to complex analysis
- The law of the iterated logarithm
- The dimension of the zero set of Brownian motion is 1/2
- Feynman-Kac formula
- Potential theory: characterization of polar sets and capacities
- Kaufman's dimension doubling theorem

For the most part, I will follow the book of Y. Peres and P. Mörters:

http://yuvalperes.com/brbook.pdf,
although it is not my intention to study this book cover to cover.

For some additional topics, I will also use Durrett's book "Brownian motion and martingales."