Probability \& its applications (Q2744060)

This is an interesting essay on the probability theory, its applications and, especially, its implications to the mathematical thinking of the 20th century. The author starts from the two principal themes of the classical probability theory, the law of large numbers and the central limit theorem, whose expression is based on independent Bernoulli trials. But, as correctly observes the author, Bernoulli trials do not occur in nature! The expression of these probability laws is derived from the idealistic view of the mathematician, while the statistician is confronted with raw observations in bulk, with ``small'' and ``large deviations'' from the mathematical models of the classical probabilistic laws. This point of view is illustrated by a series of examples of a striking diversity: (1) Information and control; (2) Geometry in high dimensions; (3) Partial differential equations; (4) Arithmetic; (5) Continued fractions; (6) Geodesic flow in negative curvature; (7) Statistical mechanics.NEWLINENEWLINEFor the entire collection see [Zbl 0966.00022].