On the relevance ofq-distribution functions: the return time distribution of restricted random walker
Makaleler > Tam Makale · 2015
Yazarlar: Jaleh Zand, Ugur Tirnakli, Henrik Jeldtoft Jensen
Journal of Physics A: Mathematical and Theoretical, Uluslararası, Wos, 2015, cilt 48, ss 425004-425004
DOI: 10.1088/1751-8113/48/42/425004
Özet
There exists 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, P R (0, t ), of a random walk on the set of integers {0, 1, 2,..., L } with a position dependent transition probability given by . We find that for all values of 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 . 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 with a 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.