Linked from

The 31 pages that link to Markov chain, each with the reason it gives.

• Population viability analysisRelated: Some viability models represent populations as transitions among discrete states.

• Stochastic processBroader topic: It is the discrete-time, discrete-state Markov case.

• Linear algebraRelated: Transition matrices encode state changes, while eigenvectors can describe long-run behavior.

• Conditional probabilityRelated: Its transition probabilities are conditional probabilities between successive states.

• Recurrence relationRelated: Transition rules recursively determine the probability distribution at each step.

• Queueing theoryNarrower topic: Markov chains provide a broader framework for analyzing queue states over time.

• Random walkRelated: A random walk is a Markov chain when its current position determines its next-step distribution.

• PageRankRelated: Web navigation becomes a Markov chain whose long-run state probabilities yield PageRank scores.

• Independent and identically distributed random variablesCompared with: Successive states are generally dependent, unlike members of an i.i.d. sequence.

• Path (graph theory)Related: A finite sequence of transitions in a state graph traces a path through possible states.

• Exponential distributionRelated: Exponential holding times underpin continuous-time Markov chains.

• Invertible matrixCompared with: Its transition matrix need not be invertible, showing that valid matrix dynamics may lose information.

• EigenvectorRelated: A stationary distribution is an eigenvector of the transition matrix with eigenvalue one.

• Bernoulli trialCompared with: State-dependent probabilities and dependence distinguish it from repeated independent Bernoulli trials.

• Convex combinationRelated: Each transition distribution is a convex combination of possible next states.

• Square matrixRelated: Transition probabilities among a finite set of states form a square matrix.

• MartingaleCompared with: The Markov property restricts dependence on past states; the martingale property restricts conditional means.

• Transition functionCompared with: It replaces a fixed next-state rule with probabilities over possible next states.

• Hidden Markov modelNarrower topic: The hidden state sequence follows this memoryless transition structure.

• Path graphRelated: A random walk on a path graph gives a Markov chain with neighboring transitions.

• Andrey MarkovBroader topic: This mathematical structure bears Markov’s name and grew from his work on dependent events.

• Gambler’s ruinNarrower topic: Fortune levels form a finite Markov chain with two absorbing states.

• Spectral radiusRelated: Eigenvalues of its transition matrix govern convergence toward stationary behavior.

• Matrix theoryRelated: A transition matrix encodes its dynamics and long-run distributions.

• Directed cycleRelated: Directed cycles in its transition graph describe possible recurring state sequences.

• Microscopic reversibilityNarrower topic: Equilibrium molecular state changes can be represented as transitions in a Markov chain.

• Snakes and LaddersRelated: A player’s next square can be modeled from the current square and the roll, including any snake or ladder.

• Eigenvalues and eigenvectorsRelated: Eigenvectors of its transition matrix describe stationary behavior and long-term evolution.

• Perron–Frobenius theoremRelated: A positive transition matrix has a unique positive stationary distribution, linked to its dominant eigenvector.

• De Finetti's theoremCompared with: Markov dependence generally differs from the conditional independence structure in the representation.

• War (card game)Related: A simplified model can ask how likely War is to end from a given configuration.