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The concept of Lyapunov exponent has long occupied a central place in thetheory of Anderson localisation; its interest in this particular context isthat it provides a reasonable measure of the localisation length. The Lyapunovexponent also features prominently in the theory of products of random matricespioneered by Furstenberg. After a brief historical survey, we describe somerecent work that exploits the close connections between these topics. We reviewthe known solvable cases of disordered quantum mechanics involving random pointscatterers and discuss a new solvable case. Finally, we point out somelimitations of the Lyapunov exponent as a means of studying localisationproperties.

Lyapunov exponents, one-dimensional Anderson localisation and products of random matrices