Stochastic calculus
Random paths, filtrations, Itô integration, stopping/localization, Itô's formula, and SDEs.
Open the primer →Log-Concave Sampling · Chapter 1
Chapter 1 Companion
Use this page when the source moves faster than your background. The main chapter remains canonical; the companion tells you which foundation to open and why it matters.
Markov semigroups
Kernels, semigroups, generators, reversibility, carré du champ, PI/LSI, and Bakry–Émery.
Open semigroup theory →Optimal transport
Couplings, transport cost, Wasserstein distance, duality, curves, and geodesics.
Open optimal transport →Wasserstein gradient flow
The conceptual bridge from Langevin dynamics to geometry on probability distributions.
Open the gradient-flow bridge →What the section pages add
Supplement only where the source is terse.
Beginner story
Each active Chapter 1 section starts from the mathematical question before introducing notation.
Hidden prerequisites
Measure-theory, integration, stopping-time, approximation, and topology lemmas are exposed where the book uses them implicitly.
Classical references
Reference packets explain which standard source supplies the background theorem and what role it plays.
Lean expansion
The exact declaration is optional. Open it only after the natural-language proof route is clear.
Reference shelf
Supplementary texts, kept below the main book.
These are supporting references already attached to audited Chapter 1 foundation packets. They explain details that Chewi can reasonably treat as background; they are not parallel replacements for Log-Concave Sampling. The shelf grows as later Chapter 1 sections receive the same source audit.
Karatzas--Shreve, Brownian Motion and Stochastic Calculus ↗
Primary rigorous Brownian-motion and filtered-probability-space reference; used to separate law, path regularity, filtration, and stopping-time hypotheses.
Used by 6 audited Chapter 1 foundation packet(s).Revuz--Yor, Continuous Martingales and Brownian Motion ↗
Secondary reference for continuous-path Brownian and continuous-martingale viewpoints, especially later version and stopping arguments.
Used by 6 audited Chapter 1 foundation packet(s).Shreve, Stochastic Calculus for Finance II ↗
Pedagogical companion for first intuition about Brownian paths, increments, Gaussian scaling, and filtrations.
Used by 4 audited Chapter 1 foundation packet(s).Protter, Stochastic Integration and Differential Equations ↗
Process-level stochastic-integration and stopping/localization framework used to design reusable interfaces beyond a single finite horizon.
Used by 3 audited Chapter 1 foundation packet(s).