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Kakutani, Shizuo, 1911–2004, Japanese mathematician, b. Osaka, Japan, grad. Tohoko Univ, Ph.D. Princeton, 1941. Kakutani repatriated to Japan during World War II, but returned to Princeton in 1948 and joined the faculty at Yale the following year, remaining there until his death. He did influential work in probability theory, particularly in the fields of ergodic theory (the use of statistical concepts to describe average properties in deterministic dynamical systems), functional analysis (a methodology used to explain the workings of a complex system), and Brownian motion. He developed the Kakutani fixed-point theorem, which was instrumental in confirming the work of mathematician John Forbes Nash and economists Kenneth J. Arrow and Gerard Debreu, all of whom were awarded the Nobel memorial economics prize. Kakutani is also known for the Kakutani skyscraper, a methodology for describing a random process, such as the tossing of a coin, that organizes the process into a picture resembling an office building, making it easier to understand the properties of the process.

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.