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This article is cited in 20 scientific papers (total in 20 papers)
REVIEWS OF TOPICAL PROBLEMS
Universal randomness
V. S. Dotsenkoab a Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre & Marie Curie, Paris VI
Abstract:
In the last two decades, it has been established that a single universal probability distribution function, known as the Tracy–Widom (TW) distribution, in many cases provides a macroscopic-level description of the statistical properties of microscopically different systems, including both purely mathematical ones, such as increasing subsequences in random permutations, and quite physical ones, such as directed polymers in random media or polynuclear crystal growth. In the first part of this review, we use a number of models to examine this phenomenon at a simple qualitative level and then consider the exact solution for one-dimensional directed polymers in a random environment, showing that free energy fluctuations in such a system are described by the universal TW distribution. The second part provides detailed appendix material containing the necessary mathematical background for the first part.
Received: July 16, 2010
Citation:
V. S. Dotsenko, “Universal randomness”, UFN, 181:3 (2011), 269–292; Phys. Usp., 54:3 (2011), 259–280
Linking options:
https://www.mathnet.ru/eng/ufn2347 https://www.mathnet.ru/eng/ufn/v181/i3/p269
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Abstract page: | 629 | Full-text PDF : | 224 | References: | 41 | First page: | 1 |
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