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@ARTICLE{Coletti:841823,
      author       = {Coletti, Cristian F. and Gava, Renato and Schütz, Gunter
                      M.},
      title        = {{C}entral limit theorem and related results for the
                      elephant random walk},
      journal      = {Journal of mathematical physics},
      volume       = {58},
      number       = {5},
      issn         = {1089-7658},
      address      = {College Park, Md.},
      publisher    = {American Inst. of Physics},
      reportid     = {FZJ-2018-00124},
      pages        = {053303},
      year         = {2017},
      abstract     = {We study the so-called elephant random walk (ERW) which is
                      a non-Markovian discrete-time random walk on ℤ with
                      unbounded memory which exhibits a phase transition from a
                      diffusive to superdiffusive behavior. We prove a law of
                      large numbers and a central limit theorem. Remarkably the
                      central limit theorem applies not only to the diffusive
                      regime but also to the phase transition point which is
                      superdiffusive. Inside the superdiffusive regime, the ERW
                      converges to a non-degenerate random variable which is not
                      normal. We also obtain explicit expressions for the
                      correlations of increments of the ERW},
      cin          = {ICS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICS-2-20110106},
      pnm          = {551 - Functional Macromolecules and Complexes (POF3-551)},
      pid          = {G:(DE-HGF)POF3-551},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000402608000030},
      doi          = {10.1063/1.4983566},
      url          = {https://juser.fz-juelich.de/record/841823},
}