Lévy flights are a type of random walk where the step lengths have a probability distribution that is heavy-tailed, often following a power law, which allows for occasional long jumps. This model is used to describe various phenomena in nature and human activities, such as animal foraging patterns, financial market fluctuations, and the spread of epidemics, due to its ability to efficiently explore space and optimize search strategies.

Lévy Flights

A random walk is a mathematical model that describes a path consisting of a succession of random steps, often used to model seemingly unpredictable processes like stock market fluctuations or molecular diffusion. It is a fundamental concept in probability theory and has applications across various fields, including physics, economics, and computer science.

Random Walk

Step lengths

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. It is fundamental in statistics and data analysis, helping to model and predict real-world phenomena by describing how probabilities are distributed over values of a random variable.

Probability Distribution

Heavy-tailed

A power law is a functional relationship between two quantities, where one quantity varies as a power of another. It is characterized by the property that a small number of occurrences are very common, while larger occurrences are rare, often visualized as a straight line on a log-log graph.

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