*We have not succeeded in answering all our problems. The answers we have found only serve to raise a whole set of new questions. In some ways we feel we are as confused as ever, but we believe we are confused on a higher level and about more important things.*

- Posted outside the mathematics reading room at Tromsø University

Notes on various topics for my own edification. The majority of material is not original and is simply a restatement of previous results in language that makes the most intuitive sense to me. Making the notes public just helps keep me accountable for their accuracy. Maybe they can also help others in the eternal quest to reduce confusion. Some wiser advice on why keeping such notes is useful comes from Ryan Giordano.

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# 2024

- 06/10 - The variational approach to concentration
- 06/08 - P-values and counterfactuals
- 05/21 - A dimension-free Bernstein bound
- 03/08 - The game-theoretic vs measure-theoretic LLN
- 03/07 - The Catoni-Giulini estimator

# 2023

- 10/28 - de Bruijn, Relative Entropy, and the CLT
- 08/23 - A Table of Exponential Inequalities
- 05/18 - Median-of-Means for Multivariate Distributions
- 04/25 - Median-of-Means for Univariate Distributions
- 03/29 - Inverting Sequential Tests
- 01/29 - Continuous Online Learning

# 2022

- 12/24 - Introduction to Differential Privacy
- 11/13 - PAC-Bayes: McAllester and Motivation
- 09/08 - Supermartingales for Nonparametric Confidence Sequences
- 08/24 - Markov for Martingales
- 07/05 - Degrees of Freedom and Stein's Estimator
- 05/31 - Liquidity Provider Wealth in Constant Product AMMs
- 05/25 - OPE in RL vs Mean Estimation in Survey Sampling
- 03/21 - Understanding Automated Market Makers (AMMs)
- 03/19 - Introduction to Game-Theoretic Probability
- 02/07 - Itô Processes and The Fundamental Theorem of Stochastic Calculus
- 01/16 - Itô Integral: Construction and Basic Properties
- 01/16 - Intuition for LP Duality