Lapinski, Tomasz Michal (2013) Limit theorems leading to Bose-Einstein, Maxwell-Boltzmann statistics and Zipf-Mandelbrot law. PhD thesis, University of Warwick.

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Abstract

In this thesis we develop the ideas introduced by V.P. Maslov in [9], [10] and [11], the new limit theorem which leads to Bose-Einstein, Maxwell-Boltzmann Statistics and Zipf-Mandelbrot Law. We independently constructed the proof for the theorem, based on Statistical Mechanics methodology, but with precise and rigorous estimates and rate of convergence. The proof involves approximation of the considered entropy, the partition function and specific Laplace type integral approximation which we had to develop specifically for this result. The proof also involved several minor estimates and approximations that are included in the work and the mathematical preliminaries which we used are attached in the appendix. In addition, we provide a step by step introduction to the underlying mathematical setting. Within the theorem we separated two cases of resulting distribution, this separation was mentioned in [11] however it was not developed further in that paper. The first case gives known distributions which are in the thesis title. Additionally, we construct two new fluctuation theorems with proof based on the proof of the main theorem. In terms of the application, we found that developed theory can be applied in the field of Econophysics. Based on the paper by F.Kusmartsev [16], we inferred that presented three distribution may correspond to the state of the economy of particular countries. Unified underlying framework might reflect the fact that these economies have one common structure.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Limit theorems (Probability theory)
Official Date:	October 2013
Dates:	Date Event October 2013 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Kolokolʹtsov, V. N. (Vasiliĭ Nikitich)
Extent:	ix, 156 pages : charts
Language:	eng

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