In this section
@article{Zand:2015:42/425004,
author = {Zand, J and Tirnakli, U and Jensen, HJ},
doi = {42/425004},
journal = {Journal of Physics A - Mathematical and Theoretical},
title = {On the relevance of q-distribution functions: The return time distribution of restricted random walker},
url = {http://dx.doi.org/10.1088/1751-8113/48/42/425004},
volume = {48},
year = {2015}
}
TY - JOUR
AB - There exist a large literature on the application of q-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, PR(0; t), of a random walk on the set of integers {0, 1, 2, ..., L} with a position dependent transition probability given by |n/L|^a. We find that for all values of a ∈ [0, 2] P_R(0, t) can be fitted by q-exponentials, but only for a = 1 is P_R(0, t) given exactly by a q-exponential in the limit L → ∞. This is a remarkable result since the exact analytical solution of the corresponding continuum model represents P_R(0, t) as a sum of Bessel functions witha smooth dependence on a from which we are unable to identify a = 1 as of special significance. However, from the high precision numerical iteration of the discrete Master Equation, we do verify that only for a = 1 is P_R(0, t) exactly a q-exponential and that a tiny departure from this parameter value makes the distribution deviate from q-exponential. Further research is certainly required to identify the reason for this result and also the applicability of q-statistics and its domain.
AU - Zand,J
AU - Tirnakli,U
AU - Jensen,HJ
DO - 42/425004
PY - 2015///
SN - 1751-8113
TI - On the relevance of q-distribution functions: The return time distribution of restricted random walker
T2 - Journal of Physics A - Mathematical and Theoretical
UR - http://dx.doi.org/10.1088/1751-8113/48/42/425004
UR - http://hdl.handle.net/10044/1/25863
VL - 48
ER -