Daniel Raban's Note Repository
I am a statistics PhD candidate at UC Berkeley, advised by Steve Evans. I received my BA in math from UC Berkeley and my 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.
Papers
- Laws of Large Numbers for Information Resolution (2025)
- How should we aggregate ratings? Accounting for personal rating scales via Wasserstein barycenters (2024)
- For a brief, non-technical overview, here's a 3-minute talk I gave on this as a UC Grad Slam semi-finalist.
- I also wrote a short (8-minute) article for a general audience.
- Here's Google NotebookLM explaining this paper as a short podcast.
- Rotatable Random Sequences in Local Fields (with Steven N. Evans, arXiv version)
Electronic Communications in Probability 24, (2019)
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
Course Notes
- Complete Notes
- Lecture 1
- Lecture 2
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- Lecture 28
- Lecture 29
- Complete Notes
- Lecture 1
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- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
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- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Complete Notes
- Lecture 1
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- Lecture 13
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- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
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- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
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- Lecture 20
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- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Lecture 29
- Lecture 1
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- Lecture 3
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- Lecture 5
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- Lecture 10
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- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Lecture 29
- Lecture 30
- Complete Notes
- Lecture 1
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- Lecture 4
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- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
- Lecture 14
- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Complete Notes
- Lecture 1
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- Lecture 4
- Lecture 5
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- Lecture 12
- Lecture 13
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- Lecture 15
- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Complete Notes
- Lecture 1
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- Lecture 4
- Lecture 5
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- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Lecture 29
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
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- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
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- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
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- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
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- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
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- Lecture 9
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- Lecture 11
- Lecture 12
- Lecture 13
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- Lecture 16
- Lecture 17
- Lecture 18
- Lecture 19
- Lecture 20
- Lecture 21
- Lecture 22
- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
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- Lecture 18
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- Lecture 20
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- Lecture 24
- Lecture 25
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- Lecture 27
- Lecture 28
- Lecture 29
- Complete Notes
- Lecture 1
- Lecture 2
- Lecture 3
- Lecture 4
- Lecture 5
- Lecture 6
- Lecture 7
- Lecture 8
- Lecture 9
- Lecture 10
- Lecture 11
- Lecture 12
- Lecture 13
- Lecture 14
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- Lecture 17
- Lecture 18
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- Lecture 23
- Lecture 24
- Lecture 25
- Lecture 26
- Lecture 27
- Lecture 28
- Lecture 29