Markov Chains and Mixing Times
by David A. Levin, Yuval Peres, Elizabeth L. Wilmer · David A. Levin, Yuval Peres
Graduate textbook on the modern theory of finite Markov chain convergence. Covers coupling, strong stationary times, spectral methods, and the cutoff phenomenon, so readers can bound how many steps a chain needs to approach its stationary distribution.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Markov Chains
probabilitycourse.com
ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Introduction to Probability Models
Standard applied probability textbook moving from conditional expectation to Markov chains, Poisson processes, continuous-time chains, renewal theory, queueing, reliability and simulation. Its many worked examples and exercises teach readers to build and analyse stochastic models of real systems.
An Intuitive Introduction to Probability
University of Zurich course taught by Karl Schmedders that builds probability from everyday examples: basic rules, conditional probability, applications, discrete random variables, and the normal distribution. Learners finish able to compute and interpret probabilities in practical decisions.