Overview of markov chains
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Overview of Markov chains. David Gleich Purdue University Network & Matrix Computations Computer Science 15 Sept 2011. Lots of words. transient recurrent primitive regular ergodic periodic irreducible P erron root. P erron vector stationary distribution

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Overview of Markov chains

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Overview of markov chains

Overview of Markov chains

David Gleich

Purdue University

Network & Matrix Computations

Computer Science

15 Sept 2011


Lots of words

Lots of words

transient

recurrent

primitive

regular

ergodic

periodic

irreducible

Perron root

Perron vector

stationary distribution

first transition analysis

Cesáro limit

reversible Markov chain

simple stationary distribution

Perron-Frobenius theorem


Some theory

Some theory

  • Theorem Let A ≥ 0 be irreducible then A has a unique positive eigenvector with eigenvalue equal to the spectral radius of A.


In german

In German

Oskar Perron, MathematischeAnnalen, 64:248-263, 1907 doi: 10.1007/BF01449896


Just kidding

Just kidding


Important application

Important application

  • PageRank

  • centrality measures

  • spectral graph theory

  • random sampling


Probable outline

Probable outline

  • Stochastic processes, Markov chains, and random walks, and stochastic matrices

  • The Perron-Frobenius theorem and stationary distribution

  • Hitting times, commute times, and other transition related problems


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