Time-averaged MSD of Brownian motion

Preprint English OPEN
Andreanov, Alexei; Grebenkov, Denis;
(2012)

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking e... View more
  • References (9)

    ϕt(s) = dy1...dymdz0...dzm

    R2m+1

    (mY−2 Z Zk(t−δ)=yk+1 [1] Weiss G H, 1994 Aspects and Applications of the Random Walk (North-Holland, Amsterdam) [2] Ben-Avraham D and Havlin S, 2000 Diffusion and reaction in disordered systems (Cambridge

    University Press) [3] Saxton M J and Jacobson K, 1997 Annu. Rev. Biophys. Biomol. Struct. 26 373 [4] Majumdar S N, 2005 Curr. Sci. 89 2076 [5] Grebenkov D S, 2007 Rev. Mod. Phys. 79 1077 [6] Bouchaud J-P and Potters M, 2000 Theory of Finantial Risks: From Statistical Physics to Risk

    Management (Cambridge University Press) [7] Qian H, Sheetz M P, and Elson E L, 1991 Biophys. J. 60 910 [8] Saxton M J, 1993 Biophys. J. 64 1766 [9] Saxton M J, 1997 Biophys. J. 72 1744 [10] Goulian M and Simon S M, 2000 Biophys. J. 79 2188 [11] Toli´c-Norrelykke I M, Munteanu E-L, Thon G, Oddershede L, and Berg-Sorensen K, 2004 Phys.

    Rev. Lett. 93 078102 [12] Golding I and Cox E C, 2006 Phys. Rev. Lett. 96 098102 [13] Arcizet D, Meier B, Sackmann E, Ra¨dler J O, and Heinrich D, 2008 Phys. Rev. Lett. 101 248103 [14] Wilhelm C, 2008 Phys. Rev. Lett. 101 028101 [15] Wirtz D, 2009 Ann. Rev. Biophys. 38 301 [16] Metzler R, Tejedor V, Jeon J-H, He Y, Deng W H, Burov S, and Barkai E, 2009 Acta Phys. Pol.

    B 40 1315 [17] Feynman R P and Hibbs A R, 1965 Quantum Mechanics and Path Integrals (New York, McGraw-

    Hill) [18] Freidlin M, 1985 Functional Integration and Partial Differential Equations, Annals of Mathematics

    Studies (Princeton University, Princeton, New Jersey) [19] Bray A J and Moore M A, 1980 J. Phys. C: Solid State Phys. 13 L655 [20] Kirkpatrick T R and Thirumalai D, 1987 Phys. Rev. B 36 5388 [21] Ruben H, 1962 Ann. Math. Stat. 33 542 [22] Ruben H, 1963 Ann. Math. Stat. 34 1582 [23] Robbins H, 1948 Ann. Math. Stat. 19 266 [24] Robbins H and Pitman E J G, 1949 Ann. Math. Stat. 20 552 [25] Pachares J, 1955 Ann. Math. Stat. 26 128 [26] Shah B K and Khatri C G, 1961 Ann. Math. Stat. 32 883 [27] Gurland J, 1953 Ann. Math. Stat. 24 416 [28] Gurland J, 1955 Ann. Math. Stat. 26 122 [29] Gurland J, 1956 Ind. J. Stat. 17 37 [30] Kotz S, Johnson N L and Boyd D W, 1967 Ann. Math. Stat. 38 823 [31] Kotz S, Johnson N L and Boyd D W, 1967 Ann. Math. Stat. 38 838. [32] Duits M H G, Li Y, Vanapalli S A, and Mugele F, 2009 Phys. Rev. E 79 051910 [33] Boyer D and Dean D S, 2011 J. Phys. A: Math. Theor. 44 335003 [34] Boyer D, Dean D S, Mejia-Monasterio C, and Oshanin G, 2012 Phys. Rev. E 85 031136 [35] Voisinne G, Alexandrou A, and Masson J-B, 2010 Biophys. J. 98 596 [36] Grebenkov D S, 2011 Phys. Rev. E 83 061117 [37] Grebenkov D S, 2011 Phys. Rev. E 84 031124 [38] Nakagawa K, 2007 IEEE Trans. Inf. Theory 53 3239 [39] Hoel P G, 1962 Introduction to Mathematical Statistics (John Wiley and Sons, New York)

  • Metrics
Share - Bookmark