@article{ŚlęzakMetzlerMagdziarz2019,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Codifference can detect ergodicity breaking and non-Gaussianity},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab13f3},
  pages     = {25},
  year      = {2019},
  abstract  = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.},
  language  = {en}
}
@article{ŚlęzakBurneckiMetzler2019,
  author    = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf},
  title     = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab3366},
  pages     = {18},
  year      = {2019},
  abstract  = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.},
  language  = {en}
}
@article{VojtaSkinnerMetzler2019,
  author    = {Vojta, Thomas and Skinner, Sarah and Metzler, Ralf},
  title     = {Probability density of the fractional Langevin equation with reflecting walls},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {100},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.100.042142},
  pages     = {11},
  year      = {2019},
  abstract  = {We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill the appropriate fluctuation-dissipation relation, the probability density on a finite interval converges for long times towards the expected uniform distribution prescribed by thermal equilibrium. In contrast, on a semi-infinite interval with a reflecting wall at the origin, the probability density shows pronounced deviations from the Gaussian behavior observed for normal diffusion. If the correlations of the random force are persistent (positive), particles accumulate at the reflecting wall while antipersistent (negative) correlations lead to a depletion of particles near the wall. We compare and contrast these results with the strong accumulation and depletion effects recently observed for nonthermal fractional Brownian motion with reflecting walls, and we discuss broader implications.},
  language  = {en}
}
@article{ThapaLukatSelhuberUnkeletal.2019,
  author    = {Thapa, Samudrajit and Lukat, Nils and Selhuber-Unkel, Christine and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {150},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {14},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.5086269},
  pages     = {18},
  year      = {2019},
  abstract  = {We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens. Published under license by AIP Publishing.},
  language  = {en}
}
@article{TeomyMetzler2019,
  author    = {Teomy, Eial and Metzler, Ralf},
  title     = {Transport in exclusion processes with one-step memory: density dependence and optimal acceleration},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {52},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {38},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ab37e4},
  pages     = {19},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{TeomyMetzler2019,
  author    = {Teomy, Eial and Metzler, Ralf},
  title     = {Correlations and transport in exclusion processes with general finite memory},
  series = {Journal of statistical mechanics: theory and experiment},
  volume    = {2019},
  journal   = {Journal of statistical mechanics: theory and experiment},
  number    = {10},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/ab47fb},
  pages     = {31},
  year      = {2019},
  language  = {en}
}
@article{SposiniMetzlerOshanin2019,
  author    = {Sposini, Vittoria and Metzler, Ralf and Oshanin, Gleb},
  title     = {Single-trajectory spectral analysis of scaled Brownian motion},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab2f52},
  pages     = {16},
  year      = {2019},
  abstract  = {Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.},
  language  = {en}
}
@article{PalyulinBlackburnLomholtetal.2019,
  author    = {Palyulin, Vladimir V. and Blackburn, George and Lomholt, Michael A. and Watkins, Nicholas W. and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.},
  title     = {First passage and first hitting times of Levy flights and Levy walks},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {21},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {10},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab41bb},
  pages     = {23},
  year      = {2019},
  abstract  = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.},
  language  = {en}
}
@article{PalyulinBlackburnLomholtetal.2019,
  author    = {Palyulin, Vladimir V and Blackburn, George and Lomholt, Michael A and Watkins, Nicholas W and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.},
  title     = {First passage and first hitting times of L{\´e}vy flights and L{\´e}vy walks},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Dt. Physikalische Ges.},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab41bb},
  pages     = {24},
  year      = {2019},
  abstract  = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.},
  language  = {en}
}
@article{PadashChechkinDybiecetal.2019,
  author    = {Padash, Amin and Chechkin, Aleksei V. and Dybiec, Bartlomiej and Pavlyukevich, Ilya and Shokri, Babak and Metzler, Ralf},
  title     = {First-passage properties of asymmetric Levy flights},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {52},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {45},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ab493e},
  pages     = {48},
  year      = {2019},
  abstract  = {L{\´e}vy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of L{\´e}vy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering L{\´e}vy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of L{\´e}vy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index and the skewness (asymmetry) parameter . The other approach is based on the stochastic Langevin equation with -stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.},
  language  = {en}
}