Optimal transportation, Shannon information, and source coding
The problem of optimal transportation of one mass into another originated with Monge in 1781, but it has been rediscovered in many guises in many branches of mathematics, science, and engineering since that time. It yields a natural notion of the distance between probability distributions, which might describe random variables, vectors, or processes. The general form of the distance is most commonly known as the transportation or Monge-Kantorovich distance, but in its long history it has acquired many other names in many fields. This talk is a mixture of history, tutorial, and survey of the idea and its applications to information theory.