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Mathematical Biology Seminar
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
2019/07/01
11:00-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Joel E. Cohen (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
Joel E. Cohen (The Rockefeller University and Columbia University)
Taylor's Law of Fluctuation Scaling
[ Abstract ]
A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
[ Reference URL ]A family of nonnegative random variables is said to obey Taylor's law when the variance is proportional to some power b of the mean. For example, in the family of exponential distributions, if the mean is m, then the variance is m^2, so the family of exponential distributions obeys Taylor's law exactly with b=2. Many stochastic processes and the prime numbers obey Taylor's law (exactly or asymptotically). Thousands of empirical illustrations of Taylor's law have been published in many different fields including ecology, demography, finance (stock and currency trading), cancer biology, genetics, fisheries, forestry, meteorology, agriculture, physics, cell biology, computer network engineering, and number theory. This survey talk will review some empirical and theoretical results and open problems about Taylor's law, including recently proved versions of Taylor's law for nonnegative stable laws with infinite mean.
https://www.rockefeller.edu/our-scientists/heads-of-laboratories/940-joel-e-cohen/
