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Let V(n) be the number of distinct points visited by a random walk on Z². V(n) approaches πn/log n asymptotically.

The maximum of a finite set of iid Gumbel random variables has a Gumbel distribution.

Cornish-Fisher expansion en.wikipedia.org/wiki/Cornish%E…

Identifying people from supposedly anonymous data johndcook.com/blog/2018/12/0…

When is correlation transitive? terrytao.wordpress.com/2014/06/05/whe…

It is the so-called 'normal' distribution that is abnormal in the sense that it has many unique properties not possessed by any other. -- E. T. Jaynes

The science of waiting in line johndcook.com/blog/2019/01/2…

The intuition behind martingales and solving problems with them codeforces.com/blog/entry/110…

The expected number of cycles in a random permutation of n items is the nth harmonic number, asymptotically log n.

Given fractions a/b and c/d, if a+d > b+c then a/b > c/d with probability 11/12. johndcook.com/blog/2021/02/2…

“In no other branch of mathematics is it so easy for experts to blunder as in probability theory.” — Martin Gardner

A Few Strange Facts About Brownian Motion cantorsparadise.com/a-few-strange-…

What do distributions in probability have to do with distributions in analysis (i.e. generalized functions)? johndcook.com/blog/2015/12/2…

Earth mover distance johndcook.com/blog/2023/11/0…

Introduction to stochastic PDEs by Fields medalist Martin Hairer hairer.org/notes/SPDEs.pdf [pdf]

Sums of uniform random values johndcook.com/blog/2009/02/1…

“We argue that stochastic differential equations are more fundamental and more relevant to modeling the world than deterministic equations.” — David Mumford

Variance matters more than mean in the extremes johndcook.com/blog/2024/08/2…

Rolling dice for normal samples johndcook.com/blog/2009/02/1…

A Straightforward Explanation of the Good Regulator Theorem lesswrong.com/posts/JQefBJDH…