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 is available at IOP
PACS: 02.50.Cw, 02.90.+p, 05.20.−y, 05.40.−a, 61.41.+e (all)
DOI: 10.3367/UFNe.0181.201103b.0269
Citation: Dotsenko V S "Universal randomness" Phys. Usp. 54 259–280 (2011)
BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks
PT Journal Article
TI Universal randomness
AU Dotsenko V S
FAU Dotsenko VS
DP 10 Mar, 2011
TA Phys. Usp.
VI 54
IP 3
PG 259-280
RX 10.3367/UFNe.0181.201103b.0269
SO Phys. Usp. 2011 Mar 10;54(3):259-280

Received: 16th, July 2010, 13th, October 2010

Оригинал: Доценко В С «Универсальная случайность» УФН 181 269–292 (2011); DOI: 10.3367/UFNr.0181.201103b.0269

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