Markov Chain

A Markov chain is a mathematical model used to describe a system that transitions from one state to another, with the probability of each subsequent state depending only on the current state and not on the sequence of events that preceded it. This property is known as the Markov property or memorylessness. Markov chains are characterized by a finite or countable number of states and transition probabilities between these states.

They are widely used in various fields, including statistical physics, economics, and computer science, particularly in algorithms involving random processes, queueing theory, and in modeling systems or processes that evolve over time in a probabilistic manner.

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In natural language processing (NLP), Markov chains can be used to generate text that mimics a particular style or author. By analyzing a corpus of text, probabilities are assigned to each possible next word based on the current word or sequence of words (state). When generating text, the algorithm selects the next word based on these probabilities, creating sentences that statistically resemble those in the original corpus.

Another example is in web page ranking algorithms like Google's PageRank, which can be conceptualized as a Markov chain where states are web pages, and transitions are the probabilities of moving from one page to another through hyperlinks, determining the 'importance' or ranking of each page.

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