If you flip a coin 1,000 times, the most likely outcome is that heads will come up 50 percent of the time. Yet it’s conceivable that heads will come up 90 percent, or even 100 percent, of the time. As the number of tosses grows, the probability of such an unlikely outcome drops off exponentially, according to precise formulas.
Although much of probability theory is concerned with figuring out what events are most likely to occur, New York University probability-theory researcher Srinivasa Varadhan focuses on the unlikely outcomes, called large deviations. Now, Varadhan has been selected to receive the Abel Prize in Mathematics for his work.
The Norwegian Academy of Science and Letters in 2001 created the prize, which includes a cash award of $850,000, to address the lack of a Nobel Prize in mathematics. The academy says that Varadhan’s work has “great conceptual strength and ageless beauty.”
Large-deviation theory has proved valuable in a wide range of applications. In the insurance industry, for example, it’s vital to calculate the likelihood that, say, a billion car crashes will occur in the United States in a year. Telecommunications providers want to know how likely it is that almost all their customers will pick up the phone at the same time.
Varadhan’s work, which offers a unified theory of large deviations, has been applied to phenomena in economics, population dynamics, traffic engineering, statistical physics, and quantum field theory. “The theory is a tour de force of many areas of mathematics,” says Tom Louis Lindstrøm, a mathematician at the University of Oslo.
The prize will be presented in Oslo on May 22.
