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Thanksgiving Latte: Matcha Apple Nut Crisp

Thanksgiving is right around the corner and what better way to celebrate than teatime with family & friends. We have a lovely Matcha latte recipe to share with you, featuring one of our new teas,  182 more words


275A, Notes 4: The central limit theorem

Let be iid copies of an absolutely integrable real scalar random variable , and form the partial sums . As we saw in the last set of notes… 7,738 more words


275A, Notes 2: Product measures and independence

In the previous set of notes, we constructed the measure-theoretic notion of the Lebesgue integral, and used this to set up the probabilistic notion of expectation on a rigorous footing. 5,661 more words


275A, Notes 0: Foundations of probability theory

Starting this week, I will be teaching an introductory graduate course (Math 275A) on probability theory here at UCLA. While I find myself using probabilistic methods routinely nowadays in my research (for instance, the probabilistic concept of… 7,799 more words


Equidistribution for multidimensional polynomial phases

The equidistribution theorem asserts that if is an irrational phase, then the sequence is equidistributed on the unit circle, or equivalently that

for any continuous (or equivalently, for any smooth) function . 2,002 more words


A differentiation identity

Here’s a cute identity I discovered by accident recently. Observe that

and so one can conjecture that one has

when is even, and

when is odd. 131 more words