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You might try Terence Tao's blog notes from his course on Perelman's proof. He assumes a basic understanding of Riemannian geometry (or at least goes over the requisite bits of it only very quickly) s …

For a fairly robust intuitive argument, think of a random walk in $\mathbb{R}^d$ as the "product" of $d$ one-dimensional walks in $\mathbb{R}^1$. For a (finite variance) random walk in $\mathbb{R}^1$, …

I'm working on a problem where I need to consider a bilinear form of the form $y^t M z$ where $M$ is an $n$-by-$n$ real symmetric matrix and $y,z \in \mathbb{R}^n$ are vectors. I also need to consider …

Let $T$ be a rooted tree with root $r$. Say an ordering $v_1,\ldots,v_n$ of the vertices of $T$ is a search order if $v_1=r$ and for all $2 \leq i \leq n$, there is $j < i$ such that $v_j$ is the pare …

In 1982, while studying the component sizes of random subgraphs of a hypercube, Ajtai, Komlós, and Szemerédi introduced a technique that came to be known as sprinkling. In this technique, the edges of …