  One of the most significant current challenges in large-scale online social
networks, is to establish a concise and coherent method able to collect and
summarize data. Sampling the content of an Online Social Network (OSN) plays an
important role as a knowledge discovery tool.
  It is becoming increasingly difficult to ignore the fact that current
sampling methods must cope with a lack of a full sampling frame i.e., there is
an imposed condition determined by a limited data access. In addition, another
key aspect to take into account is the huge amount of data generated by users
of social networking services. This type of conditions make especially
difficult to develop sampling methods to collect truly reliable data.
Therefore, we propose a low computational cost method for sampling emerging
global trends on social networking services such as Twitter.
  The main purpose of this study, is to develop a methodology able to carry out
an efficient collecting process via three random generators: Brownian, Illusion
and Reservoir. These random generators will be combined with a
Metropolis-Hastings Random Walk (MHRW) in order to improve the sampling
process. We demonstrate the effectiveness of our approach by correctly
providing a descriptive statistics of the collected data. In addition, we also
sketch the collecting procedure on real-time carried out on Twitter. Finally,
we conclude with a trend concentration graphical description and a formal
convergence analysis to evaluate whether the sample of draws has attained an
equilibrium state to get a rough estimate of the sample quality.
