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On a random walk with memory and its relation to Markovian processes (1005.3896v1)
Published 21 May 2010 in cond-mat.stat-mech and physics.ed-ph
Abstract: We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk. The time evolution of the displacement is given by an equivalent Markovian dynamical process. The probability density for the position of the walker is the same at any time as for a random walk with shrinking steps, although the two-time correlation functions are quite different.