Before revision:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium . Theoretical results are supported by numerical experiments on synthetic data, and as an example of application we discuss a strategy to mitigate the polarisation phenomenon .
After revision:  We give novel formulas based on Markov Chain analysis to compute the distribution of opinions at any time and speed of convergence to stationary equilibrium .