Shows how exponential Markov turns a tail event P(S≥t) into an optimization over λ of exp(-λt+ψS(λ)). The bottom-left plot animates the exponent f(λ) and highlights the minimizing λ*. The right panel visualizes cumulant-generating functions (ψ) and how independence makes ψ add across summands, while a quadratic (Hoeffding-style) upper bound illustrates the bounded-difference/sub-Gaussian principle that yields exponential tails.
Pure canvas 2D. Uses time-based sweep to move threshold t and re-optimize λ via coarse-to-fine grid search. CGF uses ψ(λ)=log cosh(aλ) for a bounded Rademacher variable; sum CGF scales with N and demonstrates additivity; quadratic proxy ψ≤λ^2 a^2/2 visualizes Hoeffding-type control. Blocky look via grid snapping and green-on-black palette.