Samplinglib
Lean gate passed 2026-08-19T06:04:36.257124+00:00 · 77184245109a
2.6 · Book p. 84 · PDF p. 96

Discrete Space and Time

Recasts the same ideas for discrete state spaces and discrete-time Markov chains, with their corresponding Dirichlet forms.

Open this section in the canonical August 9 source ↗

Place in the proof route

The chapter uses this material in the route toward Markov-semigroup interpolation proves functional inequalities from curvature and dissipation. The declaration-level source map is intentionally left inside the formalization layer until exact theorem anchors have been audited.

Why is this valid?

Chapter-level validity conditions

  • State whether Hessian inequalities hold everywhere, almost everywhere, or in a weak convex-analytic sense.
  • Track normalization and absolute continuity whenever a potential is used to define a probability law.
  • Keep localization inputs separate from the one-dimensional inequality they reduce to.
View Lean formalization

No declaration-level mapping has been accepted for this section. This is a route status, not a failed Lean declaration.