Math

Operator splitting

I’ll discuss the use of operator splitting as the basis for numerically solving ODEs or PDEs with some concrete examples. Along the way, we’ll stumble into a lot of linear algebra and a teensy bit of Lie theory.

Diffusing diffusivities, stochastic subordination

In this post, I’ll discuss some recent explanations for anomalous, yet Gaussian diffusion, including diffusing diffusivities and stochastic subordination.

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.