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About me

I am an associate professor of mathematics at the University of Oregon. My research interests include random spatial processes, mathematical statistical physics and number theory.

I am currently the Secretary/Treasurer of the American Association of University Professors.

Basics of Probability

Some notes on foundational ideas and definitions in modern probability theory.

Measure & Probability

We begin with the sample space $\Omega$ of a random experiment, and a $\sigma$-algebra $\mathcal H$ on $\Omega$ consisting of subsets of $\Omega$ to which we want to assign probabilities. Definition: A probability measure on… Read More »Measure & Probability

Expectation & Integral

Given a probability space $(\Omega, \mathcal H, \mathbb P)$ and positive simple random variable $X \in \mathcal H_+$, $$X = \sum_n a_n \boldsymbol 1_{A_n},$$ the expectation of $X$ is given by $$\mathbb E[X] = \sum_n… Read More »Expectation & Integral

Haar & Lebesgue Measure

Our expectations and integrals are examples of Lebesgue integrals. How do these relate to the Riemann integrals we learned about in calculus? The group of real numbers under addition $(\mathbb R, +)$ is an example… Read More »Haar & Lebesgue Measure