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Reviews of topical problems


Universal randomness

 a, b
a LPTMC, Université, Paris, France
b Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation

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.

Fulltext pdf (398 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0181.201103b.0269
PACS: 02.50.Cw, 02.90.+p, 05.20.−y, 05.40.−a, 61.41.+e (all)
DOI: 10.3367/UFNe.0181.201103b.0269
URL: https://ufn.ru/en/articles/2011/3/b/
000294813600002
2-s2.0-79959946753
2011PhyU...54..259D
Citation: Dotsenko V S "Universal randomness" Phys. Usp. 54 259–280 (2011)
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Received: 16th, July 2010, 13th, October 2010

Îðèãèíàë: Äîöåíêî Â Ñ «Óíèâåðñàëüíàÿ ñëó÷àéíîñòü» ÓÔÍ 181 269–292 (2011); DOI: 10.3367/UFNr.0181.201103b.0269

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