The element of chance enters in a crucial way not only in our daily affairs, but also in practically every branch of science. In describing the outcomes of chance, a central role is played by the Random Walker, a spirited individual who takes successive steps in random directions. The resulting trajectory, or Random Walk, has become an enduring paradigm across the sciences and mathematics.
This lecture will attempt to bring out something about the history of Random Walks; something about their properties, both intuitive and counter-intuitive; something about their wide-ranging applications in science; and something about collective effects when many Random Walkers begin to interact with each other.
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