In this thesis, the Random Energy Model (REM) is applied to the highly complex problem of random heteropolymer folding. The relevance of the REM lies in the fact that it is an analytically solvable model, which makes it possible to learn more about the (thermodynamical) behaviour of folding proteins.
Firstly, a rigorous proof of the existence of a critical point in the REM with non-zero mean is presented. The mathematical properties of the REM with non-zero mean are used to derive the thermodynamical properties of this special case of the REM, such as the free energy.
In the second part of this thesis, applications of the model to folding polymers are investigated and a simple simulation of protein folding using the REM is suggested. It turns out that this simulation is barely useful, so a more realistic version of the REM for polymer folding is suggested.