@article{SinghMetzlerSandev2020,
  author    = {Singh, Rishu Kumar and Metzler, Ralf and Sandev, Trifce},
  title     = {Resetting dynamics in a confining potential},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {53},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {50},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/abc83a},
  pages     = {28},
  year      = {2020},
  abstract  = {We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x(0). The relaxation of this system to the steady-state exhibits a dynamic phase transition, and is achieved in a light cone region which grows linearly with time. When an absorbing boundary is introduced, effecting a symmetry breaking of the system, we find that resetting aids the barrier escape only when the particle starts on the same side as the barrier with respect to the origin. We find that the optimal resetting rate exhibits a continuous phase transition with critical exponent of unity. Exact expressions are derived for the mean escape time, the second moment, and the coefficient of variation (CV).},
  language  = {en}
}
@misc{GrebenkovMetzlerOshanin2020,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {From single-particle stochastic kinetics to macroscopic reaction rates},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1018},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-48405},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-484059},
  pages     = {29},
  year      = {2020},
  abstract  = {We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.},
  language  = {en}
}
@article{GrebenkovMetzlerOshanin2020,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {From single-particle stochastic kinetics to macroscopic reaction rates},
  series = {New Journal of Physics},
  volume    = {22},
  journal   = {New Journal of Physics},
  publisher = {Dt. Physikalische Ges.},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/abb1de},
  pages     = {28},
  year      = {2020},
  abstract  = {We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.},
  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}
}