Asymptotics

Core idea

Approximations

• Stirling's approximation
• Entropy of multinomial coefficients

Asymptotic Methods

• Laplace's method
• Saddle-point method
• Method of types

Orders, expansions, and parameter estimates

• Asymptotic equivalence
• Asymptotic expansion
• Asymptotic scale
• Big-O notation
• Comparable positive functions
• Concentration scale
• Finite truncation of an expansion
• Formal expansion
• Leading order
• Little-o notation
• Absorbing logarithmic losses into a power
• Hierarchy of parameter choices
• Power law
• Uniform parameter estimate
• Perturbation
• Quadratic self-interaction
• Remainder estimate

• Leading term of an asymptotic expansion

Torus covers and support combinatorics

• Logarithmic selection of an iteration level

Residual correction and summation

• Diagonal choice of shrinking scales
• Infinite-order decay with derivatives
• Exponential decay in the square of a logarithm
• Asymptotic summation by shrinking cutoffs