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000841823 1001_ $$00000-0002-4302-8850$$aColetti, Cristian F.$$b0
000841823 245__ $$aCentral limit theorem and related results for the elephant random walk
000841823 260__ $$aCollege Park, Md.$$bAmerican Inst. of Physics$$c2017
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000841823 520__ $$aWe 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
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000841823 7001_ $$0P:(DE-HGF)0$$aGava, Renato$$b1
000841823 7001_ $$0P:(DE-Juel1)130966$$aSchütz, Gunter M.$$b2$$eCorresponding author$$ufzj
000841823 773__ $$0PERI:(DE-600)1472481-9$$a10.1063/1.4983566$$gVol. 58, no. 5, p. 053303 -$$n5$$p053303$$tJournal of mathematical physics$$v58$$x1089-7658$$y2017
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