This talk is based on two joint works with L. Decreusefond and L. Peralta.
We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance
between a random walk in $R^d$ and the Brownian motion. The proof is
based on a new estimate of the Lipschitz modulus of the solution of
the Stein's equation. Then, we quantify the rate of convergence
between the distribution of number of zeros of random trigonometric
polynomials (RTP) with i.i.d. centered random coefficients and the
number of zeros of a stationary centered Gaussian process , whose
covariance function is given by the sinc function.