Markov Chains
Markov chains are mathematical systems that model sequences of events where the probability of each event depends only on the state attained in the previous event, making them ideal for predicting random processes over time. In modern applications, they're crucial for fields like machine learning and AI, where they help in areas such as speech recognition and financial forecasting, but they can oversimplify real-world complexities if not calibrated properly.
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Markov chains power the PageRank algorithm that Google uses to rank web pages, processing over 8.5 billion searches per day and fundamentally changing how we access information online—it's estimated that this innovation contributed to Google's valuation exceeding $2 trillion. Beyond tech, they've even been applied to model the spread of diseases like COVID-19, helping predict outbreaks with startling accuracy based on just the current infection rates.
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