Collection(s) : Real life mathematics
Paru le 01/02/2020 | Cartonné 205 pages
Professionnels
Random Walks in the Plane appear very naturally, when two players flip a coin. The player who wins receives one Euro from the other, and the total gain of each player is a « random walk », given by a sequence of independent variables with same law. Conceptually speaking, this is very simple.
But such an experiment, if repeated twice, does not lead to the same results, to the same fortune, which contradicts the assumption of « repeatability » which is usually required for any experiment in Physics.
When we study the behavior of the gains, we find that (despite what most people think), they do not tend to an equilibrium ; on the contrary, Nature proceeds by large oscillations.
In this book, we introduce completely new methods for the study of these sums : they are « energy based », which means that, instead of probabilistic statements, we use tools derived from classical analysis, operator theory, special functions and trigonometry. They prove much more efficient and provide sharp quantitative results.
Bernard Beauzamy is a French mathematician, born 1949. He has been University Professor, 1979-1995. He established SCM SA in 1995, a company which does mathematical models. He has been chairman and CEO of this company since then.
