In this paper the authors prove that a random change of variable in general improves convergence properties of the Fourier expansions and they present a quantitative estimate of this phenomenon. It is well known that the best possible estimate of the Fourier partial sums \(S(n,f;x)\) for \(f\) in \(C(T)\), the continuous functions on the circle group \(T\), is given by: \(\|S(n,f;x)\|=o(\log n)\). The main idea of the paper is the following: A random perturbation should destroy the unpleasant resonance between the given function \(f\) and the Dirichlet kernel (that is the reason behind the divergence phenomenon of the Fourier series), and thus, one would hope that for a suitable change of variable \(g\) from \(T\) into \(T\), the superposition \(f\circ g\) will enjoy a better estimate than given above. In the context of the present paper, earlier related papers of \textit{A. M. Garsia} [Ann. Math., II. Ser. 79, 623-629 (1964; Zbl 0133.02702)], \textit{J. Bourgain} [Lect. Notes Math. 1376, 209-250 (1989; Zbl 0685.40001)] and \textit{S. Graf, R. D. Mauldin} and \textit{S. C. Williams} [Adv. Math. 60, 239-359 (1986; Zbl 0596.60005)] are very relevant.