Daniel Raban's Note Repository

I am a PhD student in the statistics department at UC Berkeley, advised by Steve Evans. I graduated from UC Berkeley with a BA in math and received an MA in math from UCLA. If you find any typos or inaccuracies in these notes, or if you have any suggestions on how to improve the notes (aesthetically or otherwise), please send me an email at ude.yelekreb@nabarleinad. I appreciate the help!

Why the name Pillowmath? Because it's comfy!

Misc.

• Musings About Video Game Music
• Math Tutoring Services

Expository Notes

• Measure Theory for Analysts and Probabilists (Updated 7/16/18)
• Representation Theory for Mortals (Updated 7/12/19)
• Fixed Point Theorems and the Existence of Haar Measure
• The Glivenko-Cantelli Theorem and Introduction to VC Dimension
• Topological Models of Measure-Preserving Systems (Updated 3/4/21)
• High-Dimensional Statistics and the Johnson-Lindenstrauss Embedding
• Ergodic Theorems for Spherical Averages of Free Group Actions

Papers

• How should we aggregate ratings? Accounting for personal rating scales via Wasserstein barycenters (2024; Here's Google NotebookLM explaining my paper as a short podcast.)
• Rotatable Random Sequences in Local Fields (with Steven N. Evans, 2019, arXiv)

Course Notes