TY - JOUR A1 - Eliazar, Iddo A1 - Metzler, Ralf A1 - Reuveni, Shlomi T1 - Poisson-process limit laws yield Gumbel max-min and min-max JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - “A chain is only as strong as its weakest link” says the proverb. But what about a collection of statistically identical chains: How long till all chains fail? The answer to this question is given by the max-min of a matrix whose (i,j)entry is the failure time of link j of chain i: take the minimum of each row, and then the maximum of the rows' minima. The corresponding min-max is obtained by taking the maximum of each column, and then the minimum of the columns' maxima. The min-max applies to the storage of critical data. Indeed, consider multiple backup copies of a set of critical data items, and consider the (i,j) matrix entry to be the time at which item j on copy i is lost; then, the min-max is the time at which the first critical data item is lost. In this paper we address random matrices whose entries are independent and identically distributed random variables. We establish Poisson-process limit laws for the row's minima and for the columns' maxima. Then, we further establish Gumbel limit laws for the max-min and for the min-max. The limit laws hold whenever the entries' distribution has a density, and yield highly applicable approximation tools and design tools for the max-min and min-max of large random matrices. A brief of the results presented herein is given in: Gumbel central limit theorem for max-min and min-max Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevE.100.022129 SN - 2470-0045 SN - 2470-0053 VL - 100 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Eliazar, Iddo A1 - Metzler, Ralf A1 - Reuveni, Shlomi T1 - Gumbel central limit theorem for max-min and min-max JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - The max-min and min-max of matrices arise prevalently in science and engineering. However, in many real-world situations the computation of the max-min and min-max is challenging as matrices are large and full information about their entries is lacking. Here we take a statistical-physics approach and establish limit laws—akin to the central limit theorem—for the max-min and min-max of large random matrices. The limit laws intertwine random-matrix theory and extreme-value theory, couple the matrix dimensions geometrically, and assert that Gumbel statistics emerge irrespective of the matrix entries' distribution. Due to their generality and universality, as well as their practicality, these results are expected to have a host of applications in the physical sciences and beyond. Y1 - 2019 U6 - https://doi.org/10.1103/PhysRevE.100.020104 SN - 2470-0045 SN - 2470-0053 VL - 100 IS - 2 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Krapf, Diego A1 - Metzler, Ralf T1 - Strange interfacial molecular dynamics JF - Physics today Y1 - 2019 U6 - https://doi.org/10.1063/PT.3.4294 SN - 0031-9228 SN - 1945-0699 VL - 72 IS - 9 SP - 48 EP - 54 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Teomy, Eial A1 - Metzler, Ralf T1 - Transport in exclusion processes with one-step memory: density dependence and optimal acceleration JF - Journal of physics : A, Mathematical and theoretical N2 - We study a lattice gas of persistent walkers, in which each site is occupied by at most one particle and the direction each particle attempts to move to depends on its last step. We analyse the mean squared displacement (MSD) of the particles as a function of the particle density and their persistence (the tendency to continue moving in the same direction). For positive persistence the MSD behaves as expected: it increases with the persistence and decreases with the density. However, for strong anti-persistence we find two different regimes, in which the dependence of the MSD on the density is non-monotonic. For very strong anti-persistence there is an optimal density at which the MSD reaches a maximum. In an intermediate regime, the MSD as a function of the density exhibits both a minimum and a maximum, a phenomenon which has not been observed before. We derive a mean-field theory which qualitatively explains this behaviour. KW - exclusion process KW - persistence KW - lattice gas Y1 - 2019 U6 - https://doi.org/10.1088/1751-8121/ab37e4 SN - 1751-8113 SN - 1751-8121 VL - 52 IS - 38 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Teomy, Eial A1 - Metzler, Ralf T1 - Correlations and transport in exclusion processes with general finite memory JF - Journal of statistical mechanics: theory and experiment KW - Brownian motion KW - exclusion processes Y1 - 2019 U6 - https://doi.org/10.1088/1742-5468/ab47fb SN - 1742-5468 VL - 2019 IS - 10 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Javanainen, Matti A1 - Martinez-Seara, Hector A1 - Metzler, Ralf A1 - Vattulainen, Ilpo Tapio T1 - Diffusion of Proteins and Lipids in Protein-Rich Membranesa T2 - Biophysical journal Y1 - 2018 U6 - https://doi.org/10.1016/j.bpj.2017.11.3009 SN - 0006-3495 SN - 1542-0086 VL - 114 IS - 3 SP - 551A EP - 551A PB - Cell Press CY - Cambridge ER - TY - JOUR A1 - Krapf, Diego A1 - Marinari, Enzo A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Xu, Xinran A1 - Squarcini, Alessio T1 - Power spectral density of a single Brownian trajectory BT - what one can and cannot learn from it JF - New journal of physics : the open-access journal for physics N2 - The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories. KW - power spectral density KW - single-trajectory analysis KW - probability density function KW - exact results Y1 - 2018 U6 - https://doi.org/10.1088/1367-2630/aaa67c SN - 1367-2630 VL - 20 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Gudowska-Nowak, Ewa A1 - Lindenberg, Katja A1 - Metzler, Ralf T1 - Preface: Marian Smoluchowski’s 1916 paper—a century of inspiration T2 - Journal of physics : A, Mathematical and theoretical Y1 - 2017 U6 - https://doi.org/10.1088/1751-8121/aa8529 SN - 1751-8113 SN - 1751-8121 VL - 50 IS - 38 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Metzler, Ralf T1 - Superstatistics and non-Gaussian diffusion JF - The European physical journal special topics N2 - Brownian motion and viscoelastic anomalous diffusion in homogeneous environments are intrinsically Gaussian processes. In a growing number of systems, however, non-Gaussian displacement distributions of these processes are being reported. The physical cause of the non-Gaussianity is typically seen in different forms of disorder. These include, for instance, imperfect "ensembles" of tracer particles, the presence of local variations of the tracer mobility in heteroegenous environments, or cases in which the speed or persistence of moving nematodes or cells are distributed. From a theoretical point of view stochastic descriptions based on distributed ("superstatistical") transport coefficients as well as time-dependent generalisations based on stochastic transport parameters with built-in finite correlation time are invoked. After a brief review of the history of Brownian motion and the famed Gaussian displacement distribution, we here provide a brief introduction to the phenomenon of non-Gaussianity and the stochastic modelling in terms of superstatistical and diffusing-diffusivity approaches. KW - Brownian diffusion KW - anomalous diffusion KW - dynamics KW - kinetic-theory KW - models KW - motion KW - nanoparticles KW - nonergodicity KW - statistics KW - subdiffusion Y1 - 2020 U6 - https://doi.org/10.1140/epjst/e2020-900210-x SN - 1951-6355 SN - 1951-6401 VL - 229 IS - 5 SP - 711 EP - 728 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Ala-Nissila, Tapio A1 - Metzler, Ralf ED - Metzler, Ralf T1 - Polymer translocation: the first two decades and the recent diversification JF - Soft matter N2 - Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous–infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis. KW - solid-state nanopores KW - single-stranded-dna KW - posttranslational protein translocation KW - anomalous diffusion KW - monte-carlo KW - structured polynucleotides KW - dynamics simulation KW - equation approach KW - osmotic-pressure KW - membrane channel Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76266 SN - 1744-683X VL - 45 IS - 10 SP - 9016 EP - 9037 PB - the Royal Society of Chemistry CY - Cambridge ER -