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

:    « » 181 269–292 (2011); DOI: 10.3367/UFNr.0181.201103b.0269

References (54) Cited by (16) Similar articles (20) ↓

  1. A.I. Olemskoi “Supersymmetric field theory of a nonequilibrium stochastic system as applied to disordered heteropolymers44 479–513 (2001)
  2. R. Folk, Yu. Holovatch, T. Yavorskii “Critical exponents of a three-dimensional weakly diluted quenched Ising model46 169–191 (2003)
  3. V.V. Uchaikin “Fractional phenomenology of cosmic ray anomalous diffusion56 1074–1119 (2013)
  4. G.N. Sarkisov “Molecular distribution functions of stable, metastable and amorphous classical models45 597–617 (2002)
  5. S.K. Nechaev “Problems of probabilistic topology: the statistics of knots and non-commutative random walks41 313–347 (1998)
  6. A.G. Kyurkchan, B.Yu. Sternin, V.E. Shatalov “Singularities of continuation of wave fields39 1221–1242 (1996)
  7. O.G. Bakunin “Reconstruction of streamline topology, and percolation models of turbulent transport56 243–260 (2013)
  8. E.A. Vinogradov, I.A. Dorofeyev “Thermally stimulated electromagnetic fields of solids52 425–459 (2009)
  9. O.G. Bakunin “Stochastic instability and turbulent transport. Characteristic scales, increments, diffusion coefficients58 252–285 (2015)
  10. V.F. Gantmakher, V.T. Dolgopolov “Superconductor-insulator quantum phase transition53 1–49 (2010)
  11. G.V. Kozlov, V.U. Novikov “A cluster model for the polymer amorphous state44 681–724 (2001)
  12. V.I. Klyatskin “Integral characteristics: a key to understanding structure formation in stochastic dynamic systems54 441–464 (2011)
  13. L.M. Zelenyi, A.V. Milovanov “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics47 749–788 (2004)
  14. V.I. Klyatskin “Clustering and diffusion of particles and passive tracer density in random hydrodynamic flows46 667–688 (2003)
  15. Yu.V. Gulyaev, A.S. Bugaev et alNanotransport controlled by means of the ratchet effect63 311–326 (2020)
  16. I.M. Dremin, O.V. Ivanov, V.A. Nechitailo “Wavelets and their uses44 447–478 (2001)
  17. Yu.G. Rudoi, A.D. Sukhanov “Thermodynamic fluctuations within the Gibbs and Einstein approaches43 1169–1199 (2000)
  18. A.G. Fokin “Macroscopic conductivity of random inhomogeneous media. Calculation methods39 1009–1032 (1996)
  19. N.M. Astaf’eva “Wavelet analysis: basic theory and some applications39 1085–1108 (1996)
  20. Ya.A. Smorodinskii, A.L. Shelepin, L.A. Shelepin “Groups and probabilities at the foundations of quantum mechanics35 (12) 1005–1051 (1992)

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