Stochastic limits, part 2: tails, memory, and the Joseph and Noah effects

In the previous post about limit theorems of stochastic processes, we considered when everything goes right, leading to Gaussian-like behavior. Here we’ll discuss when things go wrong, particularly when memory effects and infinite moments are introduced.

Stenger's "Proof"?

A few months ago, Frank Stenger uploaded a preprint of a proposed proof of the Riemann hypothesis. Unlike the plethora of other attempts at famous problems, nobody seems to be talking about this. Why?

Stochastic limits, part 1: CLT, Donsker’s FCLT

One way to understand the structure of randomness is to experience a lot of it. We’ll use $\lim_{n\to\infty} X_1 + \cdots + X_n$ as a case study, and along the way bump into classical ideas like the Central Limit Theorem (CLT) and Brownian motion.