@misc{GrebenkovMetzlerOshanin2021,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {Distribution of first-reaction times with target regions on boundaries of shell-like domains},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-55754},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-557542},
  pages     = {1 -- 23},
  year      = {2021},
  abstract  = {We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.},
  language  = {en}
}
@misc{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 = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {785},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43983},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439832},
  pages     = {25},
  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}
}