Why it matters

Random walks foundational. Understanding shapes many algorithms.

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The architecture

From vertex, move to random neighbor.

Cover time: visit all.

Hitting time: reach target.

Mixing time: converge to stationary.

Random walks on graphsRandom walknext = uniform neighborAnalysis metricscover + hit + mixApplicationsPageRank + SAT + morePageRank + random walk SAT + Metropolis are examples; graph structure determines behavior
Random walks.
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How it works end to end

Markov chain foundation.

Spectral gap governs mixing.

Applications: PageRank + connectivity + counting.