I’ve been reading you since The Black Swan, and what’s always drawn me in is the mathematical rigor underneath the storytelling. Your recent chapter Lindy as Distance from an Absorbing Barrier is a particularly sharp example. The reframing: that Lindy is specifically the hitting-time distribution of a driftless Brownian motion against an absorbing barrier, and that any negative drift pushes the system out of the power-law class — is a cleaner statement of the law than the folklore version.
I wrote up a walkthrough with a companion Colab that simulates all seven results from the chapter: the driftless Lévy density, the reflection principle identity, the pre-Lindy hazard hump, the Girsanov change of measure, the running sample mean divergence at μ=0\mu = 0
μ=0, and the e2μL/σ2e^{2\mu L/\sigma^2}
e2μL/σ2 non-absorption probability for positive drift (the Cagliostro formula). The math holds up cleanly under simulation.
The experiment that landed hardest for me was the running sample mean: watching the μ=0\mu = 0
μ=0 average refuse to converge while the drifted cases lock to L/μL/\mu
L/μ within a few hundred samples is a much more visceral picture of “infinite mean” than any equation. https://colab.research.google.com/drive/1jV3t5u8Jf6KxSWSHQrfG2hHpEnLLKUMi#scrollTo=v1Bj0eINsvgq
I’ve been reading you since The Black Swan, and what’s always drawn me in is the mathematical rigor underneath the storytelling. Your recent chapter Lindy as Distance from an Absorbing Barrier is a particularly sharp example. The reframing: that Lindy is specifically the hitting-time distribution of a driftless Brownian motion against an absorbing barrier, and that any negative drift pushes the system out of the power-law class — is a cleaner statement of the law than the folklore version.
I wrote up a walkthrough with a companion Colab that simulates all seven results from the chapter: the driftless Lévy density, the reflection principle identity, the pre-Lindy hazard hump, the Girsanov change of measure, the running sample mean divergence at μ=0\mu = 0
μ=0, and the e2μL/σ2e^{2\mu L/\sigma^2}
e2μL/σ2 non-absorption probability for positive drift (the Cagliostro formula). The math holds up cleanly under simulation.
The experiment that landed hardest for me was the running sample mean: watching the μ=0\mu = 0
μ=0 average refuse to converge while the drifted cases lock to L/μL/\mu
L/μ within a few hundred samples is a much more visceral picture of “infinite mean” than any equation. https://colab.research.google.com/drive/1jV3t5u8Jf6KxSWSHQrfG2hHpEnLLKUMi#scrollTo=v1Bj0eINsvgq